A transverse sinusoidal wave moves along a string in the positive… - Vidyadip

Question

A transverse sinusoidal wave moves along a string in the positive $\mathrm{x}$-direction at a speed of $10 \mathrm{~cm} / \mathrm{s}$. The wavelength of the wave is $0.5 \mathrm{~m}$ and its amplitude is $10 \mathrm{~cm}$. At a particular time $t$, the snap -shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $5 \mathrm{~cm}$ is Figure: $Image$

✓

Answer

$ \mathrm{y}=5 \mathrm{~cm} \text { and } \mathrm{V}=+\mathrm{ve} $

$ \mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t} \pm \phi) \quad \mathrm{V}=\mathrm{A} \omega \cos (\omega \mathrm{t} \pm \phi)$

We get $\omega t \pm \phi=30^{\circ}$

$ \omega=2 \pi \frac{\mathrm{v}}{\lambda}=\frac{2 \pi}{5} $

$ \mathrm{v}=\mathrm{A} \omega \cos (\omega \mathrm{t}+\phi)=\left(\frac{10}{100}\right) \times\left(\frac{2 \pi}{5}\right)\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi \sqrt{3}}{50} \mathrm{~m} / \mathrm{s}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The radii of the inner and outer spheres of a condenser are $9\,cm$ and $10\,cm$ respectively. If the dielectric constant of the medium between the two spheres is $6$ and charge on the inner sphere is $18 \times {10^{ - 9}}\;coulomb$, then the potential of inner sphere will be, if the outer sphere is earthed........$volts$

As shown in figure there is a spring block system. Block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring through $5.0\,cm$ . The spring constant is $500\,N/m$ . When released, calculate the distance where it will hit the ground $4\,m$ below the spring ? $(g = 10\,m/s^2)$

The initial velocity $v_{i}$ required to project a body vertically upward from the surface of the earth to reach a height of $10\, R ,$ where $R$ is the radius of the earth, may be described in terms of escape velocity $v_{ e }$ such that $v_{i}=\sqrt{\frac{x}{y}} \times v_{ e } .$ The value of $x$ will be ...... .

Two full turns of the circular scale of a screw gauge cover a distance of $1\ mm$ on its main scale. The total number of divisions on the circular scale is $50$. Further, it is found that the screw gauge has a zero error of $- 0.03\ mm$. While measuring the diameter of a thin wire, a student notes the main scale reading of $3\ mm$ and the number of circular scale divisions in line with the main scale as $35$. The diameter of the wire is ....... $mm$

In the figure below, $P Q R S$ denotes the path followed by a ray of light as it travels through three media in succession. The absolute refractive indices of the media are $\mu_1, \mu_2$ and $\mu_3$, respectively. (The line segment $R S$ in the figure is parallel to $P Q$ ).

Then,

To prepare a print the time taken is $5\, sec$ due to lamp of $60\, watt$ at $0.25\, m $ distance. If the distance is increased to $40 \,cm$ then what is the time taken to prepare the similar print......$sec$

The magnetic moment $\left( \mu \right)$ of a revolving electron around the nucleus varies with principal quantum number $n$ as

The energy stored in a condenser is in the form of

Consider the diagram shown below. A voltmeter of resistance $150\,\Omega$ is connected across $A$ and $B$. The potential drop across $B$ and $C$ measured by voltmeter is $...........\,V$