Question

A train whistle has a frequency of 580 Hz when stationary. If it is coming toward you at 18.8 m/s, calculate the frequency you hear.

Answer 1

The frequency you hear when the train is coming towards you is approximately 32.24 Hz.

Step-by-step explanation:

The frequency you hear when the train is coming towards you can be calculated using the formula for the Doppler effect:

f(obs) = (f(s) * (v(w) + v(s))) / v(w)

Where:

• f(obs) is the observed frequency
• f(s) is the frequency of the source (train whistle, in this case)
• v(w) is the speed of sound
• v(s) is the speed of the source (train)

Substituting the given values, we have:

f(obs) = (580 Hz * (18.8 m/s + 0 m/s)) / 340 m/s = 32.24 Hz

Therefore, the frequency you hear when the train is coming towards you is approximately 32.24 Hz.

Answer 2

The frequency you hear when the train is coming towards you is approximately 549.4 Hz.

Step-by-step explanation:

To calculate the frequency you hear when the train is coming towards you, we need to consider the Doppler effect. The Doppler effect describes the change in frequency of a wave when the source of the wave and the observer are in relative motion.

The formula to calculate the observed frequency is:

f' = f * (v + v₀) / (v + vs)

Where:

- f' is the observed frequency,

- f is the frequency of the source (580 Hz in this case),

- v is the speed of sound (approximately 343 m/s),

- v₀ is the speed of the observer (0 m/s since you are stationary), and

- vs is the speed of the source (18.8 m/s since the train is coming towards you).

Plugging in the values, we get:

f' = 580 Hz * (343 m/s + 0 m/s) / (343 m/s + 18.8 m/s)

Simplifying the equation, we find:

f' = 580 Hz * 343 m/s / 361.8 m/s

Calculating this gives us the observed frequency:

f' = 549.4 Hz

Therefore, the frequency you hear when the train is coming towards you is approximately 549.4 Hz.