Question

A truck is traveling at 74.5 kilometers per hour away from you. The driver is blowing the horn which has a frequency of 415 Hz. The speed of the sound is 346 m/s. What is the observed frequency of the sound?

Answer 1

fo = 335 Hzlet fo = frequency heard 
f = actual frequency 
v= speed of sound 
vs = speed of source 

For the first one, 
fo = fv/(v - vs) 
74.5 km/h = 20.69 m/s 
vs = -20.69m/s since it is moving away from you 

fo = (415Hz)(346m/s)/(346m/s - (-20.69m/s)) 
fo = 392 Hz 

For the second one, 
fo = fv/(v - vs) 
82.8 km/h = 23 m/s 
vs = 23m/s 

fo = (312Hz)(331m/s)/(331m/s - (23m/s)) 

Answer 2

Answer:

The observed frequency is 391.3 Hz.

Step-by-step explanation:

Given : A truck is traveling at 74.5 kilometers per hour away from you. The driver is blowing the horn which has a frequency of 415 Hz. The speed of the sound is 346 m/s.

To find : What is the observed frequency of the sound?

Solution :

Let, f be the observed frequency

$f_0=415 hz$ be the frequency heard

v=346 m/s be the speed of sound 

$v_s$ speed of truck 

Distance traveled by truck $d= 74.5 km = 74.5 \times 1000$

Time taken = 1 hour = 3600 sec.

We know, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

$v_s=\frac{74.5 \times 1000}{3600}$

$v_s=20.69m/s$

This is the Doppler effect.

The formula is given by,

$f=f_0(\frac{v}{v+v_s})$

$f=415(\frac{346}{346+20.69})$

$f=415(\frac{346}{366.69})$

$f=415(0.943)$

$f=391.345$

Therefore, The observed frequency is 391.3 Hz.