In this section assume the sound speed in air is 343 m/s.
A goose flying toward you at 12.6m/s emits a squawk, which you hear at 258Hz .
A)Find the wavelength of the sound you hear
B)Find the wavelength of the sound you hear if the goose emits the same squawk while flying away at the same speed?
A. L = V/F = 343/258 = 1.33 m.
B. F = ((Vs+Vr)/(Vs-Vg))*Fo = 258 Hz
((343+0)/(343-12.6))*Fo = 258
(343/330.4) * Fo = 258
1.0381Fo = 258
Fo = 248.5 Hz=Initial Freq. of the goose
F = ((343-0)/(343+12.6))*248.5
F = (343/355.6) * 248.5 = 239.7 Hz When
flying away.
B. L = V/F = 343/239.7 1.43 When flying away.
To find the wavelength of the sound you hear in both scenarios, we need to use the formula:
wavelength = (speed of sound) / (frequency)
A) In this case, the goose is flying toward you. The speed of sound is given as 343 m/s, and the frequency you hear is 258Hz. Plugging these values into the formula:
wavelength = 343 m/s / 258 Hz = 1.33 m
Therefore, the wavelength of the sound you hear when the goose is flying toward you is 1.33 meters.
B) Now, let's consider the scenario where the goose emits the same squawk while flying away at the same speed. The speed of sound remains the same, 343 m/s, but we need to calculate the new frequency you hear.
To calculate the frequency, we need to take into account the Doppler effect, which causes a change in frequency due to relative motion between the source of sound (the goose) and the observer (you).
The Doppler effect formula is as follows:
observed frequency = actual frequency / (1 + (velocity of source / speed of sound) * (velocity of observer / speed of sound))
In this case, the velocity of the source (the goose) is 12.6 m/s, and the velocity of the observer (you) is 0 m/s since you are stationary. Plugging in these values:
observed frequency = 258 Hz / (1 + (12.6 m/s / 343 m/s) * (0 m/s / 343 m/s))
= 258 Hz / (1 + (0.0367) * (0))
= 258 Hz
Therefore, the frequency you hear when the goose is flying away is the same as in the previous scenario, 258 Hz. Now, we can use the formula to find the wavelength:
wavelength = 343 m/s / 258 Hz = 1.33 m
Thus, the wavelength of the sound you hear when the goose is flying away at the same speed is also 1.33 meters.