A pipe closed at one end has length 0.8 m. At its open end 0.5 m long… | MHT CET 2021 (21 Sep, Shift 2)

Q92MHT CET 2021 · 21 SEP · SHIFT 2Difficult

Organ Pipes & Resonance Tube

A pipe closed at one end has length $0.8\text{ m}$ . At its open end $0.5\text{ m}$ long uniform string is vibrating in its $2$ nd harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50\text{ N}$ and the speed of sound is $320\text{ m/s}$ , the mass of the string is

Show answer and solution

Answer: (b)

Pipe fundamental: $f = \frac{v}{4L} = \frac{320}{4 \times 0.8} = 100\text{ Hz}$
String 2nd harmonic: $f = \frac{2}{2l}\sqrt{\frac{T}{\mu}} = \frac{1}{0.5}\sqrt{\frac{50}{\mu}}$
$2\sqrt{\frac{50}{\mu}} = 100 \Rightarrow \mu = 0.02\text{ kg/m}$
Mass $= \mu l = 0.02 \times 0.5 = 0.01\text{ kg} = 10\text{ g}$
So the answer is (b) 10 gram.

Report a mistake

More questions on Organ Pipes & Resonance Tube

A closed organ pipe of length ' Lc ' and an open organ pipe of length ' Lo ' contain…MHT CET 2021 (21 Sep, Shift 1)
In a resonance tube experiment when the tube is filled with water up to a height of 17.0…JEE Main 2020 (5 Sep, Shift 1)
A one metre long (both ends open) organ pipe is kept in a gas that has double the density…JEE Main 2020 (8 Jan, Shift 1)
An open organ pipe and a closed organ pipe have the frequency of their first overtone…MHT CET 2020 (16 Oct, Shift 2)
When open pipe is closed from one end third overtone of closed pipe is higher in…MHT CET 2020 (16 Oct, Shift 1)
The fundamental frequency of a closed pipe is 400 Hz. If 1/3 rd pipe is filled with…MHT CET 2020 (19 Oct, Shift 2)
A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that…JEE Main 2019 (10 Jan, Shift 2)
In a fundamental mode,the time required for the sound wave to reach upto the closed end…MHT CET 2019 (2 May, Shift 1)

Organ Pipes & Resonance Tube question from MHT CET 2021 (21 Sep, Shift 2)

More questions on Organ Pipes & Resonance Tube