A tuning fork of frequency $$440 \mathrm{Hz} $$ is attached to a long string of liner mass density $$ 0.01 \mathrm{kg} \mathrm{m}^{-1} $$ kept under a tension of $$49 \mathrm{N} $$ . The fork produces transverse waves of amplitude $$0.50 \mathrm{mm} $$ on the string. (a) Find the wave speed and the wavelength of the waves. (b) Find the maximum speed and acceleration of a particle of the string. (c) At what average rate is the tuning fork transmitting energy to the string?
f=440Hz,m=0.01kg/m,T=49N,r=0.5×10−3m
(a) v=
√
T/m
=70m/s
(b) v=λf⇒λ=v/f=16cm
(c) Paverage=2π2mv2f2=0.67W
A train moves towards a stationary observer with speed $$34\ m/s$$. The train sounds a whistle and its frequency registered by the observer is $$f_{1}$$. If the speed of the train is reduced to $$17\ m/s$$, the frequency registered is $$f_{2}$$. If speed of sound is $$340\ m/s$$, then the ratio $$f_{1}/f_{2}$$ is__?
A travelling wave is produced on a long horizontal string by vibrating an end up and down sinusoidally. The amplitude of vibration is $$1.0cm$$ and the displacement becomes zero $$200$$ times per second. The linear mass density of the string is $$0.10kg\, m^{-1}$$ and it is kept under a tension of $$90N$$. Find the velocity and acceleration of the particle at $$x=50cm$$ at time $$t=10ms$$.
A wave on a string is described by $$y(x, t)=15.0 \sin (\pi x / 8-4 \pi t)$$ where $$ x $$ and $$ y $$ are in centimeters and $$ t $$ is in seconds. What is the magnitude of the transverse acceleration for a point on the string at $$ x=6.00 \mathrm{cm} $$ when $$ t=0.250 \mathrm{s} ? $$
A wave on a string is described by $$y(x, t)=15.0 \sin (\pi x / 8-4 \pi t)$$ where $$ x $$ and $$ y $$ are in centimeters and $$ t $$ is in seconds. What is the magnitude of the maximum transverse acceleration for any point on the string?
The acceleration of this particle for$$\mid x\mid > X_{0}$$ is