B. A person on a bike is traveling along a straight street in direction due West

Question

B. A person on a bike is traveling along a straight street in direction due West, moving away from a screaming child walking in direction due East. The bike’s speed relative to the air is 4m/s, the child’s speed relative to the air is 0.8 m/s, and the sound speed in air is 340 m/s. 1.If the person on the bike observes the sound frequency of 102 Hz, what is the frequency of the sound source? 2.What is the wavelength of the sound waves in the region between the bike and the child?

Please show equations first without numbers, (I find that super helpful!) and all your work! Thanks so much!

Explanation / Answer

direction of velocity of sound (west) is positive direction.

velocity of bike wrt air = vo = 4 m/s

velocity of child wrt air = vs = - 0.8 m/s

velocity sound, vs = 340 m/s

frequency of sound observed by biker, fo = 102 Hz

When both source and observes are moving, then observed frequencyis given by, fo = fs (v - vo) / (v-vs)

So frequency of source fs = fo (v - vs) / (v - vo)

=> fs = 102 (340 + 0.8) / (340 - 4) = 103.457 Hz

the frequency of the sound source = 103.457 Hz

2. for wavelength between bike and child, e have to consider motion of child(source) only.

wavelength = (f/v) * (v-vs)/v

= (102/340) * (340 + 4) / 340 = 0.3035 m

wavelength of the sound waves in the region between the bike and the child = 0.3035 m

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