SATHEE: Wave Motion 2 Question 22

Wave Motion 2 Question 22

22. An object of specific gravity $ρ$ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is $300 H z$ . The object is immersed in water, so that one half of its volume is submerged. The new fundamental frequency (in $H z$ ) is

(a) $300 {(\frac{2 ρ - 1}{2 ρ})}^{1 / 2}$

(b) $300 {(\frac{2 ρ}{2 ρ - 1})}^{1 / 2}$

(d) $300 (\frac{2 ρ - 1}{2 ρ})$

(1995, 2M)

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Answer:

Correct Answer: 22. (a)

Solution:

The diagramatic representation of the given problem is shown in figure. The expression of fundamental frequency is

$\begin{aligned} In air \\ T = m g = (V ρ) g \\ ∴ v = \frac{1}{2 l} \sqrt{\frac{A ρ g}{μ}} \end{aligned}$

When the object is half immersed in water

$\begin{aligned} T^{'} & = m g - upthrust = V ρ g - (\frac{V}{2}) ρ_{w} g \\ = (\frac{V}{2}) g (2 ρ - ρ_{w}) \end{aligned}$

The new fundamental frequency is

$\begin{aligned} v^{'} & = \frac{1}{2 l} \times \sqrt{\frac{T^{'}}{μ}} = \frac{1}{2 l} \sqrt{\frac{(V g / 2) (2 ρ - ρ_{w})}{μ}} \\ ∴ & \frac{v^{'}}{v} & = (\sqrt{\frac{2 ρ - ρ_{w}}{2 ρ})} \\ or v^{'} & = v {(\frac{2 ρ - ρ_{w}}{2 ρ})}^{1 / 2} \\ = 300 {(\frac{2 ρ - 1}{2 ρ})}^{1 / 2} H z \end{aligned}$

Wave Motion 2 Question 22

22. An object of specific gravity $ρ$ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is $300 H z$ . The object is immersed in water, so that one half of its volume is submerged. The new fundamental frequency (in $H z$ ) is

Answer:

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Wave Motion 2 Question 22

22. An object of specific gravity ρ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is 300Hz. The object is immersed in water, so that one half of its volume is submerged. The new fundamental frequency (in Hz ) is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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22. An object of specific gravity $ρ$ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is $300 H z$ . The object is immersed in water, so that one half of its volume is submerged. The new fundamental frequency (in $H z$ ) is