A 500 Hz wave with wavelength 0.6 m travels at 300 m/s, since speed is frequency times wavelength, so this Class 11 sheet opens with the wave equation at work. The answers record 340 m/s as the speed of sound and longitudinal as the sound wave type.
Key Takeaways
A 500 Hz wave with wavelength 0.6 m travels at 300 m/s (Q1).
Sound waves in air are longitudinal (Q2).
Q3 records 340 m/s.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.A wave has a frequency of 500 Hz and a wavelength of 0.6 m. Its speed is:
3.The speed of sound in air at room temperature is approximately:
(a) 3 × 10⁸ m/s(b) 340 m/s(c) 1500 m/s(d) 34 m/s
4.Beats are produced due to the superposition of two waves of:
(a) nearly equal frequencies(b) very different frequencies(c) exactly equal amplitudes(d) exactly equal frequencies
5.In a stationary wave, the distance between two consecutive nodes is:
(a) λ(b) 2λ(c) λ/4(d) λ/2
6.For a stretched string with f = (1/2L)√(T/μ), if the tension is increased 4 times, the fundamental frequency becomes:
(a) the same(b) four times(c) two times(d) half
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Distinguish between transverse and longitudinal waves with one example of each.
8.Define wavelength, frequency and time period of a wave. Write the relation between the speed, frequency and wavelength of a wave.
9.What is a progressive wave? Write the general equation of a one-dimensional progressive wave.
10.State the principle of superposition of waves.
11.Define beats and write the expression for the beat frequency.
12.State Laplace's correction for the speed of sound in a gas.
13.What are stationary waves? Explain briefly how they are formed.
14.Define the Doppler effect and give one example from daily life.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A sound wave of frequency 440 Hz travels in air with a speed of 340 m/s. Using v = fλ, find its wavelength.
16.Two tuning forks of frequencies 256 Hz and 260 Hz are sounded together. Find the number of beats produced per second.
17.A string of length 1 m vibrates in its fundamental mode at 100 Hz. Using v = 2Lf, find the speed of the wave on the string.
18.A wave is described by y = 0.02 sin(2πx − 100πt) in SI units. Using k = 2π/λ and ω = 2πf, find its wavelength and frequency.
19.A train moving at 20 m/s blows its whistle of frequency 500 Hz. For a stationary observer ahead of the train, using f′ = fv/(v − vs) with v = 340 m/s, find the apparent frequency of the whistle.
20.A closed organ pipe has a length of 0.25 m. Using f = v/4L for the fundamental mode and v = 340 m/s, find its fundamental frequency.
Answer Key
1. c) 300 m/s
2. b) longitudinal
3. b) 340 m/s
4. a) nearly equal frequencies
5. d) λ/2
6. c) two times
7. Refer to solution guide.
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20. Refer to solution guide.
End of Worksheet
People Also Ask
How fast does a 500 Hz wave with wavelength 0.6 m travel?
300 m/s, option (c) in this worksheet (Q1).
What type of wave is sound in air?
Longitudinal, option (b) in this worksheet (Q2).
What is the speed of sound in air?
340 m/s, option (b) in this worksheet (Q3).
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