what is the minimum riding speed needed to be able to hear the whistle? Remember, you can assume the following things: The whistle you use to call your hunting dog has a frequency of 21.0 kHz, but your dog is ignoring it. You suspect the whistle may not be working, but you can't hear sounds above 20.0 kHz. The speed of sound is 330m/s at the current air temperature.
To find the minimum riding speed needed to be able to hear the whistle, we can use the concept of the Doppler effect. The Doppler effect describes the change in frequency of a sound wave relative to an observer moving towards or away from the source of the sound.
In this case, you are the observer on a horse riding towards the whistle. To hear the whistle, the frequency of the sound waves reaching your ears should be lower than 20.0 kHz, which is the highest frequency you can hear.
The equation for the Doppler effect is:
f' = f((v + v₀) / (v + vs)),
where:
f' is the observed frequency,
f is the emitted frequency (21.0 kHz),
v is the speed of sound in the air at the current temperature (330 m/s),
v₀ is the speed of the observer (your riding speed), and
vs is the speed of the source (whistle).
To find the minimum riding speed needed, we need to solve for v₀ when f' drops to 20.0 kHz.
Let's rearrange the equation to solve for v₀:
v₀ = ((f' - f) / f) * (v + vs) - v.
Substituting the given values:
f' = 20.0 kHz,
f = 21.0 kHz,
v = 330 m/s,
and vs = 0 (since the whistle is stationary),
v₀ = ((20.0 kHz - 21.0 kHz) / 21.0 kHz) * (330 m/s + 0) - 330 m/s.
Simplifying the equation:
v₀ = -0.0476 * 330 m/s - 330 m/s.
Calculating the result:
v₀ ≈ -280.13 m/s.
Since speed is a positive quantity, the minimum riding speed needed to hear the whistle is approximately 280.13 m/s.
Are you riding away from a reflecting surface and listening for the echo? If so, use the appropriate Doppler shift formula, with a received frequency of 20 kHz. Let the speed of sound be a.
The answer will be approximately
2 V/a = 1.0kHz /20 kHz = 0.05
V = (1/2)*0.05*330 = 33 m/s = 118 km/h = 74 mph