Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Waves question

2019 · 9 Apr · Shift 2 · Q44
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Waves
  5. /2019 · 9 Apr · Shift 2 · Q44

Waves question

2019 · 9 Apr · Shift 2 · Q44

JEE MainPhysicsWavesMCQ+4 / −1
A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :-
  1. A
    180m/s, 80 Hz
  2. B
    180m/s, 120 Hz
  3. C
    320m/s, 120 Hz
  4. D
    320m/s, 80 Hz
View written solutionFree

Correct answer: D

  1. Use the harmonic condition for a string fixed at both ends

For a string of length LLL fixed at both ends, the allowed wavelengths are

λn=2Ln\lambda_n = \frac{2L}{n}λn​=n2L​

where nnn is the harmonic number.

Here,

  • L=2.0 mL = 2.0\,\text{m}L=2.0m
  • third harmonic ⇒n=3\Rightarrow n=3⇒n=3
  • driving frequency f3=240 Hzf_3 = 240\,\text{Hz}f3​=240Hz

So the wavelength in third harmonic is

λ3=2L3=2×2.03=43 m\lambda_3 = \frac{2L}{3} = \frac{2\times 2.0}{3} = \frac{4}{3}\,\text{m}λ3​=32L​=32×2.0​=34​m
  1. Find the wave speed

Wave speed is

v=fλv = f\lambdav=fλ

Therefore,

v=240×43=320 m/sv = 240 \times \frac{4}{3} = 320\,\text{m/s}v=240×34​=320m/s
  1. Find the fundamental frequency

For a string fixed at both ends,

fn=nf1f_n = n f_1fn​=nf1​

So for the third harmonic,

f3=3f1f_3 = 3f_1f3​=3f1​

Given f3=240 Hzf_3=240\,\text{Hz}f3​=240Hz,

f1=2403=80 Hzf_1 = \frac{240}{3} = 80\,\text{Hz}f1​=3240​=80Hz
  1. Match with the options

We obtained:

  • wave speed =320 m/s= 320\,\text{m/s}=320m/s
  • fundamental frequency =80 Hz= 80\,\text{Hz}=80Hz

This matches Option D.

  1. Comparison with stored answer

Stored correct answer: D

Our derived answer is also D, so they agree.

PreviousNext

More from Waves

  • A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms − 1. When the car has acceleration a, the…2019 · MCQ
  • The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz, is :2019 · MCQ
  • A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close…2019 · MCQ
  • Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured in SI units. The tension in the string is :2019 · MCQ
  • A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – ω t + ϕ). Its snapshot at t = 0 is given in the figure. For this wave, the phase ϕ is : Includes diagram2019 · MCQ
  • A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound ? [Given reference intensity of sound as 10–12 W/m2 ]2019 · MCQ
  • A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, l1 = 30 cm and l2 = 70 cm. Then, v is…2019 · MCQ
  • A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?2019 · MCQ