Physics 198 Homework 9

Due October3

  1. Why it is difficult to be heard when you shout into a strong wind?

Solution:

It is because of refraction of sound. The wind speed is less near the ground than it is some distance above it. Because the speed of sound with respect to the air remains the same, the ground speed of the sound changes with altitude. The resulting refraction causes some of the sound to miss its target. So it is difficult to be heard.

  1. Why is it possible to hear around a corner but not to see around a corner?

Solution:

It is because of diffraction, which means when sound waves encounter an obstacle, they tend to bend around the obstacle. The amount of diffraction is determined by the size of the obstacle in relation to the wavelength. Because the wavelength of sound (λ=3.4m for fat100Hz) is much larger than the wavelength of light (λ=0.4μm~0.76μm), the diffraction of sound will be much more than the diffraction of light. So we can hear around a corner but we cannot see around a corner.

  1. (a) Will a lager pulse (with more energy) move faster than a smaller pulse as they travel down a rope?

(b) Will a ball thrown with more energymove faster than a ball with less energy?

(c) Does the laud sound travel faster than a softer sound?

Solution:

(a) No. The larger pulse will not move faster than the smaller pulse, because the speed of wave depends on rope tension and mass per length but not on pulse height.

(b) Yes. Because the velocity depends on the energy of the ball, the ball with more energy will move faster thanthe one with less energy.

(c) No. The speed of sound waves does not depend on the energy but only on the temperature.

  1. A trumpet player tuneshis instruments to exactly 440Hz. Find the apparent frequency due to the Doppler Effect if the player is marching (a) away from an observer (b) toward the observer. Assume that the speed of sound is 343m/s, and the speed of the payer is 1m/s.

Solution:

  1. How much will velocity of sound in a trumpet change as it warms up from room temperature to body temperature? By what percentage will the frequency change? Take into account that the wavelength remains essentially the same because the expansion of the trumpet is very small.

Solution:

The formula for the speed is: v = (331.3 + 0.606t)m/s

Room temperature:

Body temperature:

Since:

,

Change of the frequency is: 3%

  1. A thunderclap is heard 3 seconds after a lightning flash is seen. Assuming that they occurred simultaneously, how far away did that originate?

Solution:

The time taken by the light to get from lightening to person is negligible because light travels so fast. Then we can simply get the distance

  1. What is the frequency ratio between the highest and the lowest we can hear?

Solution:

The highest frequency we can hear is 20,000Hz. The lowest frequency we can hear is 20Hz.

Hence, the ratio is 1000, or more than nine octaves.

1