The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe of length L. The length of the open pipe is:
An air column closed at one end and open at the other resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column that resonates with the same tuning fork is:
A uniform rope of length L and mass m₁ hangs vertically from a rigid support, with a block of mass m₂ attached to its free (lower) end. A transverse pulse of wavelength λ₁ is produced at the lower end of the rope; when it reaches the top its wavelength is λ₂. The ratio λ₂/λ₁ is:
Three sound waves of equal amplitude have frequencies (n−1), n and (n+1) Hz. They superimpose to give beats. The number of beats produced per second is:
Two nearest (successive) harmonics of a tube closed at one end and open at the other are 220 Hz and 260 Hz. The fundamental frequency of the system is:
The fundamental frequency of an open organ pipe equals the third harmonic of a closed organ pipe. If the length of the closed pipe is 20 cm, the length of the open pipe is:
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A tuning fork produces resonance in a glass tube whose air-column length is varied by a piston. At 27 °C, two successive resonances occur at column lengths 20 cm and 73 cm. If the tuning fork frequency is 320 Hz, the speed of sound in air at 27 °C is:
A tuning fork of frequency 800 Hz produces resonance in a resonance-column tube (upper end open, lower end closed by the water surface). Successive resonances occur at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is:
In a guitar, two strings A and B of the same material are slightly out of tune and produce beats of frequency 6 Hz. When the tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B is:
If the tension in a stretched string is doubled, the ratio of the initial speed to the final speed of a transverse wave along the string is:
The 4th overtone of a closed organ pipe has the same frequency as the 3rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
The ratio of the fundamental frequency of an open pipe to that of a closed pipe of the same length is:
A pipe open at both ends has fundamental frequency f in air. The pipe is now dipped vertically into a water drum until half its length is submerged. The fundamental frequency of the air column is now:
For a travelling harmonic wave y(x, t) = 2.0 cos[2π(10t − 0.0080x + 0.35)], where x and y are in cm and t in s, the phase difference between the oscillatory motion of two points separated by 0.5 m is:
For sound waves, if the number of nodes for the $5^{\text{th}}$ harmonic of an open-ended pipe is $n$ and that for the $9^{\text{th}}$ harmonic of the same pipe with one of its ends closed is $m$, the ratio $\tfrac{n}{m}$ is:
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