Part 1: A harmonic wave is traveling along a rope. It is observed that the oscil

Question

Part 1:
A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 39.0 vibrations in 25.0 s. Also, a given maximum travels 428 cm along the rope in 10.0 s. What is the wavelength?
__cm

Part 2:
Ocean waves are traveling to the east at 4.9 m/s with a distance of 18 m between crests.
(a) With what frequency do the waves hit the front of a boat when the boat is at anchor?
__Hz

(b) With what frequency do the waves hit the front of a boat when the boat is moving westward at 1.0 m/s?
__Hz

Explanation / Answer

The no.of vibrations n = 39 in 25s

then the no of vibrations in sec f = 39/25

                                                  = 1.56Hz

The speed of the wave v = 428cm/10 = 42.8cm/s

Now v = f

therefore the wavelength

        = v/f = 42.8cm/s / 1.56

                   = 27.4 cm

(2) The speed of the waves v = 4.9m/s

the wavelength = 18m

therefore the frequency

            f = v/ = 4.9/18 = 0.272 Hz

when the boat moving with v = 1m/s

then the relative speed v = 4.9+1 = 5.9m/s

therefore the frequency f =5.9/18 = 0.327 Hz

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