Question

tudent A runs down the hallway of the school at a speed of vo=5.00m/s, carrying a ringing 1024.00-Hz tuning fork toward a concrete wall. The speed of sound is v=343.00m/s. Student B stands at rest at the wall. (a) What is the frequency heard by student B? (b) What is the beat frequency heard by student A?

Answer 1

Answer:

a) $f'=1039.15\ Hz$

b) $f_b=15.15\ Hz$

Explanation:

Given:

velocity of student A carrying the sound source, $v_s=5\ m.s^{-1}$

frequency of sound, $f=1024\ Hz$

speed of sound, $v=343\ m.s^{-1}$

(a)

Mathematical expression of Doppler-Effect is given as:

$f'=(\frac{v+v_o}{v-v_s} )f$

where:

f' = observed frequency

f = frequency of sound

$v_o=$velocity of the observer

Putting respective values in the above eq.:

$f'=(\frac{343+0}{343-5} )\times 1024$

$f'=1039.15\ Hz$

(b)

Beat frequency will be the frequency difference between the sound source and its reflection from the walls.

$f_b=f'-f$

$f_b=1039.15-1024$

$f_b=15.15\ Hz$