A boy is blowing a whistle of frequency 536 Hz and walking toward a wall with a speed of 1.64 m/s. What frequency of the reflected sound will the boy hear if the speed of sound is 343 m/s?

532 Hz

To find the frequency of the reflected sound that the boy will hear, we need to consider the Doppler effect. The Doppler effect describes the change in frequency of a wave as it is observed by an observer moving relative to the source of the wave.

The formula to calculate the observed frequency (f') of a wave due to the Doppler effect is given by:

f' = (v + v₀) / (v - vₛ) * f

Where:
f' is the observed frequency
f is the original frequency of the wave
v is the speed of sound
v₀ is the speed of the observer (boy)
vₛ is the speed of the source (whistle)

Given:
f = 536 Hz (original frequency of the whistle)
v = 343 m/s (speed of sound)
v₀ = 1.64 m/s (speed of the boy)
vₛ = -1.64 m/s (since the source is moving towards the observer, the speed is negative)

Using the formula, we can substitute the given values to find the observed frequency (f'):

f' = (343 + 1.64) / (343 - (-1.64)) * 536
f' = 344.64 / 344.64 * 536
f' = 536 Hz

Therefore, the frequency of the reflected sound that the boy will hear is 536 Hz.

To find the frequency of the reflected sound that the boy will hear, we need to take into account the Doppler effect. The Doppler effect occurs when there is relative motion between the source of sound and the observer.

In this case, the boy is both the source and the observer of the sound. He is blowing the whistle with a frequency of 536 Hz and is walking towards a wall with a speed of 1.64 m/s. The speed of sound is given as 343 m/s.

When an observer is moving towards a stationary source of sound, the frequency of the sound waves appears higher to the observer. The formula for the observed frequency (ƒ') is given by:

ƒ' = ƒ * (v + v₀) / (v - vₛ)

Where:
ƒ' is the observed frequency
ƒ is the actual frequency of the sound wave
v is the speed of sound
v₀ is the speed of the observer (in this case, the boy)
vₛ is the speed of the source of sound (in this case, the wall, which is stationary)

Plugging in the given values:
ƒ' = 536 Hz * (343 m/s + 1.64 m/s) / (343 m/s - 0 m/s)
ƒ' = 536 Hz * 344.64 m/s / 343 m/s
ƒ' = 537.69 Hz

Therefore, the frequency of the reflected sound that the boy will hear is approximately 537.69 Hz.

It is worth noting that the question states the answer is 532 Hz, which is different from the calculated value. To confirm the correct answer, it is recommended to double-check the calculations and provided information.