A dolphin sends out high-frequency sound waves to help it locate its prey. The w

Question

A dolphin sends out high-frequency sound waves to help it locate its prey. The waves bounce off a moving fish, returning to the dolphin Doppler-shifted because of the motion of the fish, and the shift in frequency tells the dolphin how fast the fish is going.

[2 points] (a) Consider the situation of sound waves emitted by a stationary dolphin that reflect off a fish while the fish is moving away from the dolphin. Choose all the correct statements: ]The frequency of waves reaching the fish is lower than the frequency emitted by the dolphin ]The frequency of waves reaching the fish is higher than the frequency emitted by the dolphin The wavelength of waves reaching the fish is longer than the wavelength coming from the dolphin I ]The wavelength of waves reaching the fish is shorter than the wavelength coming from the dolphin I ]The frequency of waves returning to the dolphin is lower than the frequency of waves reaching the fish ]The frequency of waves returning to the dolphin is higher than the frequency of waves reaching the fish 12 points] (b) Assume the fish is traveling away from the dolphin at a speed of exactly 0.0200 v, where v represents the speed of sound in water. The frequency the dolphin observes for the waves that return to the dolphin after reflecting from the fish is equal to a simple fraction multiplied by fo, where fo is the frequency of the waves emitted by the dolphin. Find this simple fraction, the ratio of the frequency returned, f, to fo in this case. (By a simple fraction, we mean a ratio of integers) The equations for two traveling waves traveling on the same string are: 21Tx (5.0 21tx cm)cos 4.0 s 8.0 mm Wave 1: y(x, t) (5.0 cm)cos Wave 2: y(x, t) 3.0 s 6.0 m 12 points] (c) Which wave has a higher speed? Neither-the waves have the same speed 1 Wave 1 1 Wave 2 Briefly justify your answer: displacements of the two waves at that instant) [1 pointl (d) When is the next time at which the net displacement at x 0 m is +10.0 cm? [1 point (e) At t 0 s, how far from x 0 m is the closest point that also has a net displacement o +10.0 cm?

Explanation / Answer

a)
the options are true

1)the frequency of waves reaching the fish is lwoer than the frequency emitted by the dolphin

2)the wavelength of waves reaching the fish is longer than the wavelength coming from the dolphin

and

3) The frequency of waves returning to the dolphin is lower than the frequency of waves reaching the fish.

b)

   speed of fish is vf = 0.02 v ==> 0.02*1484 m/s = 29.68 m/s

f0 is freqeuncy of the waves emitted by the dolphin and f is frequency returned to the dolphin

f is < f0

   f /f0 is a less than one

c)
higher speed is

y(x,t) = a cos (kx-Wt)
  
k = 2pi/ Lambda , W = 2pi *f

here k1 = -2pi/6 = 2pi/lambda ==> lambda1 = 6 m,

k2 = -2pi/8 = 2pi/lambda ==> lambda2 = 8 m,

w = 2pi*f = 2pi*v/ lambda

if lambda is more the W is less so less speed
so the heigher speed is for y1(x,t), first wave has higher speed

d)

given wave functions y(x,t) = 5 cm cos (2pit/3 - 2pix/6)

       y(x,t) = 5 cm cos (2pit/4 - 2pix/8)

5cos(2pi*t/3)+5cos (2pi*t/4) = 10, t = 0 s only

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