Single Choice

The equation of a wave travelling on a stretched string is : $$y=4\sin 2\pi \left(\dfrac{t}{0.02}-\dfrac{x}{100}\right)$$ Here $$x$$ and $$y$$ are in $$cm$$ and $$t$$ is in second. The speed of wave is :

A$$50\ m/s$$
Correct Answer
B$$40\ m/s$$
C$$50\ cm/s$$
D$$40\ cm/s$$

Solution

Speed of the wave is $$\dfrac{\omega}{k}$$ where $$\omega$$ is coefficient of $$t$$ and $$K$$ is coefficient of $$x$$.
Substituting to the values with proper units as given in the question, we get
$$\dfrac{\omega}{k}$$ = $$\dfrac{100}{0.02}$$ cm/s= 50 m/s

SIMILAR QUESTIONS

Physical World

A wire of length $$L$$ and mass per unit length $$6.0\times 10^{-3}kgm^{-1}$$ is put under tension of $$540\ N$$. Two consecutive frequencies that it resonates at are: $$420\ Hz$$ and $$490\ Hz$$. Then $$L$$ in meters is:

Physical World

If a progressive wave is represented as $$y=2\sin \pi \begin{pmatrix}\dfrac{t}{2}-\dfrac{x}{4}\end{pmatrix}$$ where x is in metre and t is in second, then the distance travelled by the wave in 5 s is

Physical World

The dimensional formula of magnetic flux is :

Physical World

Two stings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed '$$V_A$$' and on string B with speed '$$V_B$$'. The ratio $$\dfrac{V_A}{V_B}$$ is

Physical World

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 speed and the wavelength of the wave.

Physical World

A sonometer wire having a length of $$1.50 m$$ between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire?

Physical World

Three resonant frequency of a string are $$90, 150$$ and $$210 Hz$$. If the length of the string is $$80 cm$$, what would be the speed of a transverse wave on this string?

Physical World

Along a stretched string equation of transverse wave is $$y=3\sin \left[2\pi \left(\dfrac{x}{20}-\dfrac{t}{0.01}\right)\right]$$ where, $$x, y$$ are in $$cm$$ and $$t$$ is in $$sec$$. The wave velocity is :

Physical World

The speed of wave of time period $$T$$ and propagation constant $$k$$ is:

Contact Details