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__?
$$f_{app} = f_{0}\left [\dfrac {v_{2} \pm v_{0}}{v_{2}\mp v_{s}}\right ]$$
$$f_{1} = f_{0}\left [\dfrac {340}{340 - 34}\right ]$$
$$f_{2} = f_{0} \left [\dfrac {340}{340 - 17}\right ]$$
$$\dfrac {f_{1}}{f_{2}} = \dfrac {340 - 17}{340 - 34} = \dfrac {323}{306}\Rightarrow \dfrac {f_{1}}{f_{2}} = \dfrac {19}{18}$$.
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?
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