A string of length 40cm and weighing 10g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160N/m and is stretched by 1.0cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring?
Question types
Wave Motion and Waves on a String question types
80 questions across 5 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
80
Questions
5
Question groups
5
Question types
01
3 Marks Question
23 Q→021 Marks Question
9 Q→034 Marks Questions
2 Q→04M.C.Q (1 Marks)
32 Q→055 Marks Questions
14 Q→Sample Questions
Wave Motion and Waves on a String questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
View full solution →
A steel wire of mass 4.0g and length 80cm is fixed at the two ends. The tension in the wire is 50N. Find the frequency and wavelength of the fourth harmonic of the fundamental.
A 2 in long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200m/s and thee amplitude is 0.5cm.
- Find the wavelength and the frequency.
- Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50cm has reached its maximum displacement.
A string of length 20cm and linear mass density 0.40g/cm is fixed at both ends and is kept under a tension of 16N. A wave pulse is produced at t = 0 near an end as shown in figure, which travels towards the other end.
- When will the string have the shape shown in the figureagain
- Sketch the shape of the string at a time half of that found in part (a).
Two long strings A and B, each having linear mass density 1.2 x 10-2kg/m, are stretched by different tensions 4.8N and 7.5N respectively and are kept parallel to each other with their left ends at x = 0. Wave pulses are produced on the strings at the left ends at t = 0 on string A and at t = 20ms on string B. When and where will the pulse on B overtake that on A?
Show that the particle speed can never be equal to the wave speed in a sine wave if the amplitude is less than wavelength divided by $2\pi.$
View full solution →What is the smallest positive phase constant which is equivalent to $7.5\pi?$
View full solution →A wave is represented by an equation $\text{y}=\text{c}_1\sin(\text{c}_2\text{x}+\text{c}_3\text{t}).$ In which direction is the wave going ? Assume that c1, c2 and c3 are all positive.
View full solution →Show that for a wave travelling on a string:
View full solution →$\frac{\text{y}_\text{max}}{\text{u}_\text{max}}=\frac{\text{v}_\text{max}}{\text{a}_\text{max}},$
Where the symbols have usual meanings. Can we use componendo and dividendo taught in algebra to write,$\frac{\text{y}_\text{max}+\text{v}_\text{max}}{\text{y}_\text{max}-\text{v}_\text{max}}=\frac{\text{v}_\text{max}+\text{a}_\text{max}}{\text{v}_\text{max}-\text{a}_\text{max}}?$
If the speed of a transverse wave on a stretched string of length 1m is 60m/s, what is the fundamental frequency of vibration?
The radio and TV programmes, telecast at the studio, reach our antenna by wave motion. Is it a mechanical wave or nonmechanical?
A 4.0kg block is suspended from the ceiling of an elevator through a, string having a linear mass density of 19.2 × 10-3kg/m. Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2.0m/s2. Take g = 10m/s2.
Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be:
View full solution →- A
- 2A
- 4A
- $\sqrt{2}\text{A}.$
The fundamental frequency of a string is proportional to:
- Inverse of its length.
- The diameter.
- The tension.
- The density.
Velocity of sound in air is 332m/s. Its velocity in vacuum will be:
- > 332m/s
- = 332 m/s
- < 332m/s
- Meaningless.
Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for:
- Both the velocity and the kinetic energy.
- The velocity but not for the kinetic energy.
- The kinetic energy but not for the velocity.
- Neither the velocity nor the kinetic energy.
A cork floating in a calm pond executes simple harmonic motion of frequency v when a wave generated by a boat passes by it. The frequency of the wave is:
View full solution →-
$\text{v}$
-
$\frac{\text{v}}{2}$
-
$2\text{v}$
-
$\sqrt{2}\text{v}.$
A wave is described by the equation
View full solution →$\text{y}=(1.0\text{mm})\sin\pi\Big(\frac{\text{x}}{2.0\text{cm}}-\frac{\text{t}}{0.01\text{s}}\Big).$
- Find the time period and the wavelength.
- Write the equation for the velocity of the particles. Find the speed of the particle at x = 1.0cm at time t = 0.01s.
- What are the speeds of the particles at x = 3.0cm, 5.0cm and 7.0cm at t 0.01s?
- What are the speeds of the particles at x 1.0cm at t = 0.011, 0.012, and 0.013s?
Two waves, each having a frequency of 100Hz and a wavelength of 2.0cm, are travelling in the same direction on a string. What is the phase difference between the waves,
- If the second wave was produced 0.015s later than the first one at the same place.
- If the two waves were produced at the same instant but the first one was produced a distance 4.0cm behind the second one?
- If each of the waves has an amplitude of 2.0mm, what would be the amplitudes of the resultant waves in part (a) and (b)?
The equation of a wave travelling on a string stretched along the X-axis is given by-
View full solution →$\text{y}=\text{A}\text{e}^{-\Big(\frac{\text{x}}{\text{a}}+\frac{\text{t}}{\text{T}}\Big)^2}.$
- Write the dimensions of A, a and T.
- Find the wave speed.
- In which direction is the wave. travelling?
- Where is the maximum of the pulse located at t = T? at t = 2T?
A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at t = to is given by $\text{g}(\text{x},\text{t}_0)=\text{A}\sin\big(\frac{\text{x}}{\text{a}}\big).$ Write the wave equation for a general time t.
View full solution →A particle on a stretched string supporting a travelling wave, takes 5.0ms to move from its mean position to the extreme position. The distance between two consecutive particles, which are at their mean positions, is 2.0cm. Find the frequency, the wavelength and the wave speed.
Generate a Wave Motion and Waves on a String paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.