1. ⇒ (MHT CET 2023 11th May Evening Shift )

Two progressive waves are travelling towards each other with velocity $50 m / s$ and frequency $200 Hz$ . The distance between the two consecutive antinodes is

A. $0.125 m$

B. $0.150 m$

C. $0.175 m$

D. $0.200 m$

Correct Option is (A)

Velocity of wave, $v = f λ$

$∴ λ = \frac{v}{f} = \frac{50}{200} = 0.25 m$

$∴$ Dividing the wavelength for antinodes:

$\begin{aligned} λ & = \frac{0.25}{2} \\ = 0.125 m \end{aligned}$

2. ⇒ (MHT CET 2023 11th May Morning Shift )

A string fixed at both the ends forms standing wave with node separation of $5 cm$ . If the velocity of the wave on the string is $2 m / s$ , then the frequency of vibration of the string is

A. 0.2 Hz

B. 10 Hz

C. 20 Hz

D. 40 Hz

Correct Option is (C)

Separation between consecutive nodes, $\frac{λ}{2} = 5 cm$

$∴ λ = 10 cm = 0.1 m$

The frequency of vibration is given as:

$n = \frac{v}{λ} = \frac{2}{0.1} = 20 Hz$

3. ⇒ (MHT CET 2023 10th May Morning Shift )

In case of a stationary wave pattern which of the following statement is CORRECT?

A. The distance between the consecutive nodes is equal to the wavelength.

B. In a pipe at both ends only even harmonics are present in an air column.

C. In a pipe closed at one end, all harmonics are present in an air column.

D. In case of a stretched string when vibrated, frequency of first overtone is same as second harmonic.

Correct Option is (D)

Frequency of first harmonic $= n = \frac{v}{λ} = \frac{1}{2 l} \sqrt{\frac{T}{m}}$

Frequency of second harmonic $= 2 n = \frac{1}{l} \sqrt{\frac{T}{m}}$ ..... (i)

For the first overtone, $λ = l$

$∴$ Frequency of first overtone $n_{1} = \frac{1}{l} \sqrt{\frac{T}{m}}$ ...... (ii)

Comparing (i) and (ii), $n_{1} = 2 n$

4. ⇒ (MHT CET 2023 9th May Evening Shift )

Stationary waves can be produced in

A. only solid and gaseous media

B. only liquid and gaseous media

C. only solid and liquid media

D. solid, liquid and gaseous media

Correct Option is (D)

Currently no explanation available

⇒Superposition of Waves