Question
A 1.0 kg block is attached to a spring with spring constant 16 N/m and is at rest on a smooth horizontal plane. It is hit with a hammer and acquires instantaneously a speed of 0.40 m/s. The amplitude of the subsequent oscillations is A transverse sinusoidal wave with amplitude 0.01 m and frequency 10 Hz travels at 200 m/s in the positive x - direction, At I = 0 s the point x_3 = 1.00 m is a crest of the wave. The function y(x, t) that describes the wave is A stretched string fixed at two ends has a mass of 0.08 kg and a length of 8.00 m. The tension in the string is 64.0 N. There exists a standing wave on the string. For the third harmonic, the vibration frequency is You were at rest and a police car with its siren on was passing you with a constant speed. You force that the frequencies of the siren were respectively 550 Hz and 450 Hz when the police car was moving toward and away from you. Assume that the speed of sound in air is 340 m/s. the speed of the police car was problem 1(9) shows a ring of radius R with a narrow gap of 1 (1
Explanation / Answer
5. this acquired speed is the maximum speed.
and total energy = m Vmax^2 / 2 = kA^2/2
1 * 0.40^2 = 16 A^2
A = 0.10 m or 10 cm
6. A = 0.01 m
f = 100 Hz
v = 200 m/s
y(x,t) =A sin(kx - wt + phi )
w = 2pif = 200pi rad/s
lambda = v / f = 200 / 100 = 2 m
k = 2pi/lambda = pi
at t= 0, x = 1m , y = A
A = A sin( pi (1) - 0 - phi)
sin(pi - phi) = 0
pi - phi = pi/2
phi = pi/2
y(x,t) =0.01 sin(pix - 200pi t + pi/2 )
