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physics Advanced Subsidiary (AS) Level Physics.
 
Solved problems for the chapter:
 

Progressive waves

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Progressive Longitudinal Wave
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Progressive Transverse Wave
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Water Waves
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:progressive_waves/4053/


Example 1.

The speed of propagation of longitudinal waves on a coil spring is . The spring is excited longitudinally with a frequency of 100 Hz and compressions and rarefactions are observed. What will be the distance between two adjacent compressions?

    
Example 2.

The source of a longitudinal wave oscillates with a frequency of 50 Hz. The wave propagates along a spring. At time 0 s, the particles are initially in equilibrium. At a time of 58 ms and at a distance of 0.6 m, the deviation of the particles from the equilibrium position is 6 mm. At what amplitude do the particles oscillate at the source if the speed of the wave is ?

    
3.

Are the following statements correct?

  • We observe longitudinal waves on a coil spring. At the compressions, the displacement of the particles from the equilibrium position is zero.

  • At the rarefactions, the displacement of particles from the equilibrium position is greatest.

  • A sound source oscillates according to the oscillation of the displacement from the equilibrium position at the beginning of the spring.

  • A sound source fluctuates the same as the compressions of the rings at the beginning of the spring.

  • The positions of the compression and the rarefaction on the spring do not change.

  • A coil spring can only oscillate longitudinally.

    
4.

Waves are created on the water surface with the help of two springs, which are separated by 20 cm. The wave sources oscillate at a frequency of 3 Hz, but not in the same phase. The wave caused by the first source leads the second by a quarter of a wavelength. Observing the interference of the two waves far from the source, at what angles, relative to the bisector between the two sources, do the waves add up (interfere constructively)? The speed of the waves is 0.4 m/s.

    
5.

A speaker vibrates at a frequency of 680 Hz and emits a sound wave. The figure shows the compressions and rarefactions of the air and the displacement of the air particles from the equilibrium position as a function of the distance from the speaker in zero seconds.




What is the displacement of the particles from the equilibrium position in 1 ms at a distance of 1.3 m from the speaker? The velocity of the wave in the air is 340 , and the amplitude from the equilibrium position is 10 nm.

    
6.

A longitudinal wave propagates along a spring and its motion is described by the equation:




Calculate the amplitude, frequency, wavelength, and speed of the wave?

    
7.

Using the wave graph given below, determine the amplitude, wavelength, and frequency of the wave. The wave travels to the right at a speed of .


Progressive transverse wave

    
8.

A progressive transverse wave on a rope is excited at one end of the rope by means of a pendulum oscillating at a frequency of . The distance between two ridges of the pendulum is . What is the speed of the wave?

    

9.

A long taut rope is hit twice a second and the progressive transverse wave produced travels along the rope at a speed of . What is the distance between two successive crests of the wave?

    
10.

A string is tensioned with a force of . A transverse wave propagates along the string at a speed of . What is the mass per unit length of the rope?

    
11.

Calculate the diameter of a steel wire tensioned with a force of if a transverse wave propagates along the wire at a speed of ? The density of steel is .

    
12.

A load of mass is hung on a thin wire weighing . The length of the wire is . We hit the rope transversely with our fingers so that a wave is formed. At what speed does the wave propagate along the wire?

    
13.

A wire is passed over two pulleys as shown in the figure below. A load of mass 6 kg is hung on each end of the wire. The wire has a mass of per meter of length. If a wave is propagated along the wire, at what speed does the wave travel?


Progressive Transverse Wave

    
14.

A long rope is tied to two trees and tensioned with a force of . The weight of the rope is . The rope is then hit at one end and the wave generated travels from that end to the other and bounces back. How long will it take for the wave to return to its starting point?

    
15.

On a long rope, two wavefronts travel toward each other at a speed , as shown in the figure below. The amplitude of the first wavefront is and that of the second is . What is the shape of the rope when the two wavefronts overlap (when the bisectors of the wavefronts are aligned)?


    
16.

A wave is generated on a rope and the distance between a crest and the trough after it is . Calculate the distance traveled by the wave in three oscillation times.

    
17.

A wave travels a distance of in two seconds. The distance between the two successive troughs is .

  • At what frequency is the wave excited?

  • What distance does the wave travel in ?

  • What distance does it travel in two oscillation periods?

    
18.

We observe a wave traveling to the right along a rope. At some point, an image of the wave is captured when the red sticker on the rope is on the crest of the wave as shown in the figure below.




  • Draw an image of this wave after 1/4 of the oscillation period.

  • Draw an image of the wave when it is shifted by 1.5 wavelengths.

  • How does the red sticker on the rope swing?

    

19.

The wave speed on a tensioned rope is . The rope is tensioned with a force of . By how much do we need to change the force to increase the wave speed by ?

    
20.

A wave bounces off the shore and moves towards an anchored ship. It bounces off the ship again and returns to shore. The time taken for the wave to return back to the shore is 6 s. If the average depth of the sea is 3 m, what is the distance of the ship from the shore?

    
21.

Tsunamis are destructive waves generated by an underwater earthquake or volcanic eruption. The wavelength of the wave is usually very large. Suppose it is 500 m long. How long does it take for the wave to reach the land, 400 km away?

    
22.

A sea wave with an amplitude of 0.2 m and a wavelength of 2 m travels from deep water towards the shallows along the shore. The water in the shallows is 0.5 m deep.

  • Calculate the wave velocity in deep and shallow water.

  • What is the wavelength of the wave in shallow water?

  • Is the wave sinusoidal?