Physics chapter 4

Find the difference in the fundamental frequency, calculated with and without the end correction, of an open organ pipe 2 m long and 10 cm in diameter.

f=v/2L 𝐿𝑒𝑐 = 𝐿 + 2(0.61)𝑟

In order to lower the Helmholtz resonances of a guitar, would you make the sound hole larger or smaller?

larger sound hole produces a greater neck area, and therefore a higher resonance (see Helmholtz formula in chapter 2)

Sympathetic vibration

one vibrator causing another to vibrate at the same frequency (which may or may not be a resonant frequency) an example is a piano string causing the bridge and soundboard to vibrate at the strings frequency

Can a singer break a wineglass by singing loudly?

perhaps

Linewidth

the width delta f of a resonance curve, usually measured at 71 % of it max height; a measure of sharpness of a resonance (a sharp resonance is characterized by a small line width)

Resonance

when a vibrator is driven by a force that oscillates at a frequency at or near natural frequency of the vibrator, relatively large amplitude results

Q

a parameter that denotes the sharpness of a resonance; Q=f0/ delta f, where f0 is the resonance frequency and delta f is the line width

Spectrum

a recipe for vibratory motion (or sound) that specifies the relative amplitudes of the partials

Damping

energy loss in a system that slows it down or leads to a decrease in amplitude

Soundboard

a sheet of wood or other material that radiates a substantial amount of sound when it is driven in sympathetic vibration by a vibrating string or in some other manner

What does n equal in Figure 4.5 (d)? How many wavelengths equal L?

11 nodes, L = 5λ or λ = L/5

Phase difference

a measure of the relative positions of two vibrating objects at a given time; also the relative positions in a vibration cycle of a vibrating object and a driving force

Harmonic

a mode of vibration (or a component of a sound) whose frequency is a whole number multiple of the fundamental frequency

A pipe with one open and one closed end has its lowest resonance at 200Hz. What are the frequencies of its next two resonances?

a closed pipe resonates with overtones that are odd multiples of the fundamental. If the fundamental is 200 Hz, the next two resonances are given by: f3 = 3f1 = 3(200 Hz) = 600 Hz f5 = 5f1 = 5(200 Hz) = 1000 Hz

Overtone

a component of a sound with a frequency greater than the fundamental frequency

Partial

a component of sound; includes the fundamental plus the overtone

Helmholtz resonator

a vibrator consisting of a volume of enclosed air with an open neck or port

A string is fastened at both ends and its first overtone has a frequency of 300 Hz. What is the fundamental frequency? a. 150 Hz b. 100 Hz c. 600 Hz d. 300 Hz

a. 150 Hz

Distinguish between partials, harmonics, and overtones.

all components of sound. the first one includes the fundamental, plus the overtones, the third one has a frequency greater than the fundamental, and the second one is a mode of vibration whose frequency is a whole-number multiple of the fundamental frequency.

Determine the frequencies of the fundamental and the first overtone (second partial) for the following. Neglect end corrections. of 16 ft stopped organ pipe (one open end, one closed end)

also in notes

A vibrating string is 0.5 meters long, a linear density of 0.001 kg/m and is stretched with a tension of 10 N. What is its fundamental frequency? 𝑣 = √ T/𝜇 𝑓 = 𝑣 / 𝜆 a. 200 Hz b. 100 Hz c. 50 Hz d. 10 Hz

b. 100 Hz

A pipe with that is open on both ends has its lowest resonance at 100 Hz. What are the frequencies of its next two resonances? a. 50 Hz, 25 Hz b. 200 Hz, 300 Hz c. 300 Hz, 500 Hz d. 200 Hz, 400 Hz

b. 200 Hz, 300 Hz

A pipe with that is closed on one end has its lowest resonance at 100 Hz. What are the frequencies of its next two resonances? a. 50 Hz, 25 Hz b. 200 Hz, 300 Hz c. 300 Hz, 500 Hz d. 200 Hz, 400 Hz

c. 300 Hz, 500 Hz

To excite a singing rod in its fundamental mode, where should you hold it? Where should you stroke it?

hold the rod at the center where the node is, stroke towards the ends

Determine the frequencies of the fundamental and the first overtone (second partial) for the following. Neglect end corrections. of a 16 ft open organ pipe

in notes

What is acoustic impedance?

is t the ratio of sound pressure to the volume velocity

What is the main function of a piano soundboard?

radiation from a vibrating string is greatly enhanced by the sympathetic vibration of the soundboard

If you blow over the ends of two pipes, one with the other end closed and one with it open, which pipe will give the tone of lower pitch? Approximately how much lower?

the closed end pipe will be one octave lower, because it vibrates with half the fundamental frequency

Electromagnetic force

the force that results from the interaction of an alternating electric current with a magnetic field

Fundamental

the mode of vibration (or component of a sound) with the lowest frequency

In Figure 4.4, do the solid curves or the dashed curves represent a higher Q? Explain.

the solid line has a higher Q value, the higher the damping, the less abrupt the phase change is, and therefore the lower the Q.

Write a definition of resonance and give several examples.

when a vibrator is driven by a force that oscillates at a frequency at or near the natural frequency of the vibrator, and a relatively large amplitude results. Examples: Child on a swing, standing waves in a pipe or string.

A nylon guitar string 65 cm long has a mass of 8.3x10^-4 kg/m and the tension is 56N. Find the frequencies of the first four partials.

𝑣=√𝑇/mu f=v/2L