Oscillations and Waves Problems

Using the date from the above graph, deduce for this sound wave: the wavelength

0.5m

Using the date from the above graph, deduce for this sound wave: the amplitude

0.5mm

State the amplitude of the vibrations (maximum displacement)

0.6mm

Diagram 1 represents equally spaced beads on a spring. The beads are 1 cm apart. Which of the following is the best estimate of the amplitude?

0.8 cm

State and explain two reasons why the graph opposite indicates that the object is executing simple harmonic motion.

1. The displacement is proportional to the acceleration because the graph is a straight line through the origin. 2. The displacement is in the opposite direction to the acceleration (meaning restoring it to the origin) as seen by the negative slope.

The diagrams below show two standing wave patterns that are set up in a stretched string fixed at both ends. The frequency of pattern 1 is f1 and that of pattern 2 is f2. The ratio (f1/f2) is

1/3

Determine how far the wave has moved in (T/4)s.

5/4=1.25cm

(b)(ii) The frequency of source S is varied. Explain why, at a particular frequency, the powder is seen to form small, equally-spaced heaps in the tube.

A standing wave is formed in the tube. Heaps will form at the nodes (areas of no vibration) while the antinodes (areas of maximum vibration) will help push the powder toward the nodes and away from the antinodes.

The motion of the object gives rise to a longitudinal progressive (travelling) sound wave. State what is meant by a longitudinal progressive wave.

A wave whose particles vibrate parallel to the direction of energy propagation.

Describe, by reference to the propagation of energy, what is meant by a transverse wave.

A wave whose particles vibrate perpendicular to the direction of energy propagation.

A water surface wave (ripple) is travelling to the right on the surface of a lake. The wave has period T. The diagram below shows the surface of the lake at a particular instant of time. A piece of cork is floating in the water in the position shown. Which is the correct position of the cork a time (T/4) later?

A. (the cork at the crest moves downward the length of the amplitude when moving to the right)

A standing wave is established on a string between two fixed points. At the instant shown, point T is moving downwards. Which arrow gives the direction of movement of point U at this instant?

D (U is between a crest and a trough, a little less than 1.5 wavelength to the right of T, so it moves down)

A wave is travelling through a medium. The diagram shows the variation with time t of the displacement of a particle of the medium from t=0 to t=25 ms. Which of the following correctly gives the frequency and the amplitude of the wave?

Frequency/Hz: 50 Amplitude/cm: 1.0

A string with both ends fixed is made to vibrate in the second harmonic mode as shown by the dashed lines in the diagram below. The solid line shows a photograph of the string at a particular instant of time. Two points on the string have been marked P and Q. Which of the following correctly compares both the period of vibration of P and Q and the average speed of P and Q?

Period: same Average speed: different

Outline the conditions necessary for the formation of a standing (stationary) wave.

Superposition of two waves moving in opposite direction with the same frequency and amplitude.

Deduce the wavelength of the wave.

T = 0.3ms f = 1/(0.3x10(^-3) = 3333Hz v=fλ 380= 3333λ λ= 0.11m

The experiment in (b)(ii) is repeated on a day when the temperature of the air in the tube is higher. The mean separation of the heaps is observed to have increased for the same frequency of the source S. Deduce qualitatively the effect, if any, of the temperature rise on the speed of the sound in the tube.

The further apart the heaps are, the larger the wavelength, so the speed increases causing the kinetic energy to increase and therefore the temperature will increase.

Which one of the following is correct for transfer of energy along a standing wave and for amplitude of vibration of the standing wave?

Transfer of energy along a standing wave: None Amplitude of vibration of the standing wave: Variable amplitude

*Use data from the graph to show that the frequency of oscillation is 350 Hz.

a = -w(^2)x -w(^2) = a/x = slope (-0.52, 2500) (0.54, -2600) 2500-2600ms(^-2) ------------------------ -0.52-0.54mm 5100ms(^-2) ---------------- -1.06x10(^3)m =-4.8x10(^6)s(^-2)= -w(^2) =2193.4s(^-1) = w = 2πf f= 349Hz = 350Hz

Two pipes P and Q are of the same length. Pipe P is closed at one end and pipe Q is open at both ends. The fundamental frequency (first harmonic) of the closed pipe P is 220Hz. The best estimate for the fundamental frequency of the open pipe Q is

closed -> open = 2x the length 440Hz

The graph below shows the variation of air pressure with distance along a wave at one given time. The arrow indicates the direction of travel of the wave. The air pressure at point P is

decreasing

State one example, other than a wave on a string, of a transverse wave.

electromagnetic waves (light)

The period of the wave is 1.2x10(^-3)s. Deduce that the speed of the wave is 250ms(^-1).

f = 1/T f = 1/(1.2x10(^-3)s) = 833Hz v=fλ v=(833)(0.30m)= 249.9 = 250ms(^-1)

For a standing wave, all the particles between two successive nodes have the same

frequency only

7. The displacement d of a particle in a wave varies with distance x along a wave and with time t as shown below. Which expression gives the speed of the wave.

l/2τ

State whether this wave is an example of a longitudinal (sound) wave or a transverse (light/electromagnetic) wave.

longitudinal

Standing waves in an open pipe come about as a result of

reflection and superposition

A standing wave is established in air in a pipe with one closed and one open end. The air molecules near X are

sometimes at the centre of a compression and sometimes at the centre of a rarefaction

*The wavelength of a progressive transverse wave is defined as

the distance moved by a wavefront during ONE oscillation of the source

*The speed of a wave is defined as

the speed of transfer of the energy of the wave

Determine the wavelength of the wave is 5.0 cm and its speed is 10 cms(^-1).

v = fλ f=v/λ f= (10cms(^-1))/(5.0cm) f=2.0 Hz

The speed of the wave is 330ms(^-1). Using the answer in "Use the data from the graph to show that the frequency of oscillation is 350 Hz," calculate the wavelength of the wave.

v = λf 330 = 350λ λ = 0.94m

A pipe, open at both ends, has a length L. The speed of sound in the air in the pipe is v. The frequency of vibration of the fundamental (first harmonic) standing wave that can be set up in the pipe is

v/2L

Using the date from the above graph, deduce for this sound wave: the speed

v=8λ v=660(0.5) v= 330 ms(^-1)

(b) The distance between the supports is 1.0m (2.0m wavelength). A wave in the string travels at a speed of 240ms(^-1). Calculate the frequency of the vibration of the string.

v=fλ f=v/λ f= 240ms(^-1)/(2.0m) f=120Hz

An organ pipe that is open at one end has the same fundamental frequency as the string in part (b). The speed of sound in air is 330ms(^-1). Determine the length of the pipe.

v=fλ v=f(4L) (330)/(120*4)=120(4L)/(120*4) L=0.69m

A tube is filled with water and a vibrating tuning fork is held above its open end. The tap at the base of the tube is opened. As the water runs out, the sound is loudest when the water level is a distance x below the top of the tube. A second loud sound is heard when the water level is a distance y below the top. Which one of the following is a correct expression for the wavelength λ of the sound produced by the tuning fork?

λ= 2(y-x)

The mean separation of the heaps of powder in (b)(ii) is 9.3cm when the frequency of the source S is 1800 Hz. Calculate the speed of sound in the tube.

λ= 2x9.3cm = 18.6cm=0.186m v=fλ v=1800(0.186)= 334.8ms(^-1) = 330ms(^-1)