# SLHS 2156Q Problem Sets (1-4)

Please match the scale of measurement to the appropriate data set. Nominal Ordinal Interval Ratio

Nominal: purple, purple, blue, green, orange, green Ordinal: A+, A, A-, B+, B, B-, C+, C, C-, D, F Interval: 0°F, 32°F, 50°F, 75°F, 100°F Ratio: 1", 2", 6", 12", 36"

If the duration of a tone is decreased by 1/15, by how much will the power need to decrease to maintain the same level of signal energy?

None of the above

Please express 3.2588 x 10^-2 in conventional notation.

0.032588

Calculate the pressure in Pascals, if a force of 10N is applied uniformly to an area of 200m2.

0.05

Solve: log10 4 ^3

1.8063

What is the wavelength of a sine wave traveling through air at 20°C with a frequency of 175 Hz?

1.96

Solve: antilog10^4

10,000

Solve: antilog10^5

100,000

Please calculate the angular velocity in radians per second for a sine wave with a frequency of 750 Hz.

4,712.4

If the Weber fraction (for frequency discrimination) for frequencies between 500 and 3000Hz is a constant value, approximately .3%, what is the threshold frequency difference (jnd) for a tone with a frequency of 1500Hz?

4.5 Hz

What is the root-mean-square (rms) amplitude of a sine wave with a peak-peak amplitude of 14Pa?

4.949

If a 750 msec tone has a power of 45 dB, what is its energy?

43.75 dB

Solve: log2^64

6

Calculate the level in decibels (re: 10-12 watts/m2) that results if one source with an intensity of 2 x 10-6 is combined with a source that has an intensity of 5 x 10-6

68.5

If the background noise in a cafeteria is 65 dB SPL, yet a student's personal FM system provides a +6 dB SNR, at what level is the signal being presented?

71 dB

9^3

729

Calculate the acceleration of a car traveling 65 m/s, which then slows to 60 m/s in a span of 20 seconds.

- 0.25

What is the amplitude in decibels (re: the amplitude of the fundamental) for the sixth harmonic of a sawtooth wave in which the amplitude of the fundamental frequency is 5V?

-15.6 dB

If a signal is presented at 45 dB SPL in background noise of 70 dB SPL, what is the resulting SNR?

-25 dB

What is the amplitude in decibels (re: the amplitude of the fundamental) of the third component of a triangular wave in which the amplitude of the fundamental frequency is 3V?

-28 dB

Find the dB SPL if the pressure ratio is 1:2

-6

If the signal is presented at 10-5 watt/m2, and the noise is at 8 x 10-5 watt/m2, what is the SNR in dB?

-9 dB

If R=5Ω and Xm=12Ω, what is the impedance of the system?

13

6 runs were measured of a patient's threshold using both ascending and descending method of limits. The thresholds found were at 14 dB, 11 dB, 17 dB, 10 dB, 15 dB, & 12 dB. What is the patient's estimated threshold?

13 dB

Find the dB IL if the intensity ratio is (2.45 x 10^1):1

13.9

What are the approximate upper & lower cutoff frequencies for a 1-octave filter with a center frequency of 920 Hz?

1300 Hz & 605 Hz

What is the momentum of the 5 kg object, traveling at an average velocity of 3 m/s?

15

If a patient's threshold is 75 dB SPL at 1500 Hz, and the same tone is uncomfortably loud at 90 dB SPL, what is their dynamic range at this frequency?

15 dB

The subject indicated that they perceived a tone at 15 dB, 17 dB, 15 dB, 12 dB, 15 dB, & 12 dB. At what level was the sound heard 50% of the time?

15 dB

Solve: antilog2^4

16

Solve: log4.4 (4.4 ^ 16)

16

What is the bandwidth of a filter curve with a center frequency of 775 Hz and an upper cutoff frequency of 862 Hz, presuming the upper and lower cutoff frequencies are equidistant from the center frequency?

174 Hz

Please calculate the angular velocity in radians per second for a sine wave with a frequency of 3000 Hz.

18,849.6

What is the pressure ratio of a sound wave that is 46 dB SPL?

2 x 10^2

Please express 247912 in scientific notation.

2.47912 x 10^5

Solve: log10^543

2.7348

Approximately how much is: log10^630

2.8

Find the dB SPL if the pressure ratio is (10-3/10-4)

20

If the complex sound wave takes 2 ms to complete one cycle of vibration, what is the 3rd overtone of the sound wave?

2000 Hz

If the natural frequency of a system is 700 Hz and the stiffness is increased by a factor of 9:1, what is the resulting frequency?

2100 Hz

If a signal is presented at 35 dB SPL with a signal-to-noise ratio (SNR) of +12 dB, what is the level of background noise?

23 dB

Please calculate the fourth harmonic of a periodic sound wave with a fundamental frequency of 60 Hz.

240 Hz

Solve: 2^3 x 2^5

256

If the fundamental frequency of a soundwave is 130 Hz, what are its corresponding harmonics?

260 Hz, 390 Hz, 520 Hz, 650 Hz, etc.

Imagine an object traveling at 90 m/s. Its speed then increases to 120 m/s, in a span of 10 seconds. What is its acceleration?

3

What is the rms voltage for the first four components of a triangular wave in which the amplitude of the fundamental frequency is 3V?

3, 0.33, 0.12, 0.06

What is the root-mean-square (rms) amplitude, in units of Pa, of a sine wave with a maximum amplitude of 5 Pa?

3.535

Calculate dB IL re: 10-12 watts/m2 if Ix=10-9. In other words, for a reference intensity of 10-12 watts/m2

30

Using the information from question 5, what is the point of subjective equality?

30.75 dB SPL

Please calculate the fourth overtone of a periodic sound wave with a fundamental frequency of 60 Hz.

300 Hz

Two tones are presented at an equal level. One is at 3050 Hz, and one at 3055 Hz. At what frequency will we perceive the modulated (beating) tone?

3052.5 Hz

Find the dB SPL if the pressure ratio is 40:1

32

Solve: antilog10^1.5315

34

Using the equation given at the top of Yost, Fig. 11.8 (that is, ERB (Hz) = 24.7(4.37f(kHz)+1), what is the ERB at 3000 Hz?

349 Hz

If the pressure of a sound source that has dB SPL of 32.4 is doubled, what is the new sound pressure level?

38.4

If the frequency of a sine wave is 250 Hz, what is the period (in ms)?

4

What is the intensity ratio of a soundwave that is 56 dB IL?

4 x 10 ^5

If the duration of the tone from question 14 was decreased to 250 msec, and energy is to remain the same, at what level is the power?

49.85 dB

At what frequency will the perceived tone in question 17 beat (wax and wane)?

5 Hz

If the period of a sine wave is 200ms, what is the frequency?

5 Hz

What is the intensity ratio of a soundwave that is -23 dB IL?

5 x 10^-3

What is the rms voltage for the first four components of a square wave in which the amplitude of the fundamental frequency is 5V?

5, 1.66, 1.0, 0.714

What is the center frequency of a 1-octave bandwidth filter with a lower cutoff frequency of 35 Hz and an upper cutoff frequency of 70 Hz?

50 Hz

How much work (in joules) has been accomplished if 10N of force is applied to an object over a distance of 5 meters?

50.0

If the natural frequency of a system is 2000 Hz and the mass is increased by a factor of 16:1, what is the resulting frequency?

500Hz

Using this table, what is a patient's threshold (in dB SPL) if their measured threshold is 42 dB HL under insert earphones at 250 Hz?

56 dB SPL

What, in units of Pascals, is the peak-peak amplitude of a sine wave that has an instantanous amplitude at 90° of 3Pa?

6

What is the sound pressure (in μPa) if the sound wave is 50 dB SPL re: 2 x 101 μPa?

6.32 x 10^3

The method of limits was used to determine a subject's differential thresholds. The average upper limen was 34 dB SPL. The average lower limen was 27.5 dB SPL. What is the interval of uncertainty?

6.5 dB SPL

A pulse train has a pulse repetition frequency of 200 Hz and a pulse duration of 3 ms. What proportion of each period is occupied by each pulse?

60%

Using the same table given in question 8, if a patient's threshold is 54 dB SPL under inserts at 4000 Hz, what is their expected threshold (in dB SPL) at 4000 Hz under supra-aural headphones?

60.5

Given the curve, at what approximate level is the subject's 0.5 probability threshold?

68 dB

Calculate dB SPL re: 2 x 101 μPa if Px=8 x 104 μPa

72

If a patient's threshold is 16 dB SPL at 1500 Hz, and the same tone is uncomfortably loud at 95 dB SPL, what is the patient's dynamic range at this frequency?

79 dB

If the period of a sine wave is 125ms, what is the frequency?

8 Hz

Find the dB IL if the intensity ratio is 7:1.

8.5

Solve: (3^16.25/3^12.25)

81

If the F0 is 275 Hz, what are the next three harmonics needed to create a square wave?

825 Hz, 1375 Hz, 1925 Hz

Calculate dB SPL re: 2 x 101 μPa if Px=4.25 x 105 μPa

86.6

What is the bandwidth of a filter curve with an upper cutoff frequency of 1650 Hz and a lower cutoff frequency of 712 Hz?

938 Hz

Which two tones will produce the "best beating" sensation?

950 Hz & 954 Hz

What is the mass reactance (in ohms) of a system with a frequency of 2 kHz and effective mass of 0.1 kg?

1,256.64

How much force (Newtons) is needed to move a 5 kg object from a speed of 0 m/s to a speed of 3 m/s in 15 seconds?

1.0

Please express 0.122187 in scientific notation.

1.22187 x 10^-1

What is the Half-Wave Rectified Average Amplitude of a sine wave with a maximum amplitude of 5Pa?

1.59

A subject's differential thresholds were found to have an average upper limen of 62 dB SPL and an average lower limen of 58.5 dB SPL. What is the just-noticeable difference for this subject?

1.75 dB SPL

Calculate the average speed (in m/s) of a person who has walked 6.6 km in one hour.

1.8

If a pulse train has a period of 25 ms and a pulse duration of 5 ms, where is the fifth null in the envelope?

1000 Hz

What is the frequency of a sine wave that has a period of 0.001s?

1000Hz

What is the wavelength of a sine wave traveling through air at 0°C with a frequency of 3 Hz?

110.3

Using the figure given, what is the approximate dynamic range at 3 kHz between sensitivity in sound field and the threshold of discomfort?

120 dB

A complex, periodic waveform with energy at odd and even harmonics has a fundamental period of 5 ms. What is the frequency of the 6th harmonic?

1200 Hz

What is the period of a sine wave that has a frequency of 2000 Hz?

.0005 seconds

If the frequency of a sine wave is 50 Hz, what is the period?

.02 seconds