Problem 1 : A vertical spring stretches by 10 cm when a 1,2 kg block is hung on

Question

Problem 1 : A vertical spring stretches by 10 cm when a 1,2 kg block is hung on it. The block is then displaced an additional 6 cm downwards and released from rest. a) Show that the spring constant k is 120 N/m b) Find the time period and the maximum speed of resulting SHM c) Find the total mechanical energy of the oscillating system? d) When the block is 3 cm below its equilibrium position and moving downwards, find its velocity and the magnitude and direction of its acceleration. Problem 2 : Two point sources of sound wave are 60 cm apart. They produce sinusoidal sound wave in phase and with equal amplitude. Consider a large circular path around the sources a) When you walk once around the circle, you detect exactly 12 maxima and 12 minima in the intensity pattern. Whatis the wavelength of the sound wave ? b) Is there a wavelength for which you would detect 10 maxima and 10 minima? If so, what wavelength? Problem 3 : A steel wire is 80 cm long, has mass 16g and is strectched by a tension of 3200 N a) Find the speed of wave on the wire b) Find the frequency of its fundamental mode of vibration c) If the wire vibrates in its fundamental mode with an amplitude of 6 mm at the antinode , find the maximum transverse velocity of the wire d) Find the frequency and wavelength of the fourth harmonic e) How many harmonics of the wire could be heard by a person able to hear the frequencies up to 20kHz Problem 4 : 1 metre from a source, the sound level is 120 dB . At what distance is it 50 dB?

Explanation / Answer

From Hooke's Law F = k*x so k = F/x = 1.20*9.8/0.0260 = 1176N/m W = 1/2*k*x^2

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