A pipe 30 cm long is open at both ends. Which harmonic mode of the pipe is resonantly excited by a 1.1 kHz source? (Take the speed of sound in air = 330 ms^–1) 

1. First

2. Second

3. Third

4. Fourth

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude ${\rho }_0$ inside the tube. If the atmospheric pressure is ${\rho }_A$ , then the ratio of maximum and minimum pressure at the closed end of the tube will be :

1. $\frac{({\rho }_A+{\rho }_0)}{({\rho }_A-{\rho }_0)}$

2. $\frac{({\rho }_A+2{\rho }_0)}{({\rho }_A-2{\rho }_0)}$

3. $\frac{{\rho }_A}{{\rho }_A}$

4. $\frac{\left({\rho }_A+\frac{1}{2}{\rho }_0\right)}{\left({\rho }_A-\frac{1}{2}{\rho }_0\right)}$

Two closed pipe produce 10 beats per second when emitting their fundamental nodes. If their length are in ratio of 25 : 26. Then their fundamental frequency in Hz, are :

(1) 270, 280

(2) 260, 270

(3) 260, 250

(4) 260, 280

If v is the speed of sound in the air then the shortest length of the closed pipe which resonates to a frequency n :

(1) $\frac{v}{4n}$

(2) $\frac{v}{2n}$

(3) $\frac{2n}{v}$

(4) $\frac{4n}{v}$

The frequency of fundamental tone in an open organ pipe of length 0.48 m is 320 Hz. The speed of sound is 320 m/sec. Frequency of fundamental tone in closed organ pipe will be : 

1. 153.8 Hz

2. 160.0 Hz

3. 320.0 Hz

4. 143.2 Hz

What is the minimum length of a tube, open at both ends, that resonates with tuning fork of frequency 350 Hz? [velocity of sound in air = 350 m/s] 

1. 50 cm

2. 100 cm

3. 75 cm

4. 25 cm

The harmonics which are present in a pipe open at one end are :

1. Odd harmonics

2. Even harmonics

3. Even as well as odd harmonics

4. None of these

The stationary wave $y=2a\sin kx\cos \omega t$ in a closed organ pipe is the result of the superposition of $y=a\sin (\omega t-kx)$ and

(1) $y=-a\cos (\omega t+kx)$

(2) $y=-a\sin (\omega t+kx)$

(3) $y=a\sin (\omega t+kx)$

(4) $y=a\cos (\omega t+kx)$

An open pipe of length l vibrates in the fundamental mode. The pressure variation is maximum at :

(1) l/4 from ends

(2) The middle of the pipe

(3) The ends of the pipe

(4) At l/8 from ends of pipe

The fundamental frequency of pipe is 100 Hz and the other two frequencies are 300 Hz and 500 Hz then :

(1) The pipe is open at both the ends

(2) The pipe is closed at both the ends

(3) One end open and another end is closed

(4) None of the above