Question:
A string of length \(1\text{ m}\) and mass \(490\text{ g}\) is put under a tension of \(25\text{ N}\). A wave of frequency \(120\text{ Hz}\) is sent along it. The speed of this wave is
A string of length \(1\text{ m}\) and mass \(490\text{ g}\) is put under a tension of \(25\text{ N}\). A wave of frequency \(120\text{ Hz}\) is sent along it. The speed of this wave is
Show Hint
For transverse waves on a stretched string,
\[
v=\sqrt{\frac{T}{\mu}}
\]
where \(\mu=\frac{m}{L}\) is the mass per unit length.
Updated On: Jun 25, 2026
- \(7.14\text{ ms}^{-1}\)
- \(0.71\text{ ms}^{-1}\)
- \(0.51\text{ ms}^{-1}\)
- \(51.0\text{ ms}^{-1}\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Use the formula for wave speed on a stretched string.
Wave speed on a stretched string is given by \[ v=\sqrt{\frac{T}{\mu}} \] where \[ T=\text{tension in the string} \] and \[ \mu=\text{mass per unit length} \]
Step 2: Calculate linear mass density.
Given: \[ m=490\text{ g}=0.49\text{ kg} \] \[ L=1\text{ m} \] Therefore, \[ \mu=\frac{m}{L} \] \[ \mu=\frac{0.49}{1} \] \[ \mu=0.49\text{ kg m}^{-1} \]
Step 3: Substitute into the wave speed formula.
Given tension: \[ T=25\text{ N} \] Thus, \[ v=\sqrt{\frac{25}{0.49}} \] \[ v=\sqrt{51.02} \] \[ v\approx 7.14\text{ ms}^{-1} \]
Step 4: Final conclusion.
Therefore, the speed of the wave is \[ \boxed{7.14\text{ ms}^{-1}} \]
Wave speed on a stretched string is given by \[ v=\sqrt{\frac{T}{\mu}} \] where \[ T=\text{tension in the string} \] and \[ \mu=\text{mass per unit length} \]
Step 2: Calculate linear mass density.
Given: \[ m=490\text{ g}=0.49\text{ kg} \] \[ L=1\text{ m} \] Therefore, \[ \mu=\frac{m}{L} \] \[ \mu=\frac{0.49}{1} \] \[ \mu=0.49\text{ kg m}^{-1} \]
Step 3: Substitute into the wave speed formula.
Given tension: \[ T=25\text{ N} \] Thus, \[ v=\sqrt{\frac{25}{0.49}} \] \[ v=\sqrt{51.02} \] \[ v\approx 7.14\text{ ms}^{-1} \]
Step 4: Final conclusion.
Therefore, the speed of the wave is \[ \boxed{7.14\text{ ms}^{-1}} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Wave Motion Questions
- If the speed of a wave doubles as it passes from shallow water into deeper water, its wavelength will be
- The frequency of a wave is 500 Hz and its wavelength is 0.66 m. What is the speed of the wave?
- The ratio of radii of two wires is 1:2 and the density of their materials are in the ratio 1:4. If same tension is applied to both the wires then the ratio of the speed of transverse waves produced in them is:
- A wave is represented by \( y = 0.1 \sin(200t - 10x) \). Find wave velocity.
- A source of sound moves towards a stationary observer with speed \( 10 \text{ m/s} \). Speed of sound = \( 340 \text{ m/s} \). If original frequency is \( 340 \text{ Hz} \), apparent frequency is:
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions