Waves

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be:

The equation of a transverse wave travelling along a string is $y(x,t)=4.0\sin \left[20\times {10}^{-3}x+600t\right]\mathrm{mm}$, where \(x\) is in mm and \(t\) is in second. The velocity of the wave is :

[JEE Main 2025, 23 Jan (Shift 2)]

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \(\rho_1\) and \(\rho_2\), respectively. The frequency of $9^{\text{th }}$ harmonic of closed tube is identical with $4^{\text{th }}$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ${\rho }_1:{\rho }_2=1:16$, then the length of the open tube is :

[JEE Main 2025, 22 Jan (Shift 1)]

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be:

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason R

Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the correct answer from the options given below.

A closed organ pipe of length $10 \, \text{cm}$ is in the $9^{\text{th}}$ harmonic and resonates with the $4^{\text{th}}$ harmonic of an open organ pipe. Find the length of the open organ pipe.

Statement-I : Velocity of sound in solids in more compared to that in gases.

Statement-II : Bulk modulus of gas is more than that of solids.

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \(\rho_1\) and \(\rho_2\), respectively. The frequency of $9^{\text{th }}$ harmonic of closed tube is identical with $4^{\text{th }}$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ${\rho }_1:{\rho }_2=1:16$, then the length of the open tube is :

[JEE Main 2025, 22 Jan (Shift 1)]

Statement-I : Velocity of sound in solids in more compared to that in gases.

Statement-II : Bulk modulus of gas is more than that of solids.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason R

Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the correct answer from the options given below.