Answer to Question #310556 in Electricity and Magnetism for Diablo

Question

A train moves from an observer standing on a platform with a velocity of 10m/s. The siren emitted by the Train has a frequency of 50Hz.

A. What is the frequency of the sound heard by the observer?

B. What is the frequency of the sound heard by the observer in the Train?

(SPEED OF SOUND = 330 PER SECONDS)

Answer 1

Formula Doppler effect

$$\nu=\nu_{0} \cdot \frac{v+v_1}{v-v_2}$$

$\nu$ - frequency of sound heared by observer

$\nu_0$ - frequency of sound from source

$v$ - velocity of sound

$v_1$ - velocity of observer when it move to the source (else it will be negative)

$v_2$ - velocity of source when it move to the observer ( else it will be negative)

Answer A

$$\nu=\nu_0 \frac{v}{v-v_2}$$

Calculating

$$\nu=50 \frac{330}{330-(-10)}=48,5 Hz$$

Answer B

$$\nu=\nu_0 \frac{v+v_1}{v-v_2}$$

The observer moves in train

$$v_1=v_2$$

Calculating

$\nu=50 \cdot\frac{330+10}{330-(-10)}=50 Hz$