An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ............... cm.
An ultrasound signal of frequency 50 KHz is sent vertically down into a medium. The signal gets reflected from a depth of 25 mm and returns to source 0.00005 seconds after it is emitted. The wavelength of the ultrasound signal in that medium is ............... cm.
Show Hint
Correct Answer: 1.99 - 2.01
Solution and Explanation
Step 1: Understanding the formula for wave speed.
The wave speed \( v \) of the ultrasound in the medium can be found using the formula: \[ v = \frac{\text{distance}}{\text{time}} \] The signal travels to the depth and back, so the total distance is \( 2 \times 25 \, \text{mm} = 50 \, \text{mm} = 0.05 \, \text{m} \).
Step 2: Calculating the wave speed.
The time taken for the wave to travel this distance is \( 0.00005 \) seconds. Therefore, the wave speed is: \[ v = \frac{0.05 \, \text{m}}{0.00005 \, \text{s}} = 1000 \, \text{m/s} \]
Step 3: Finding the wavelength.
The wavelength \( \lambda \) is related to the wave speed \( v \) and frequency \( f \) by the formula: \[ v = f \lambda \] Substitute the known values: \[ 1000 \, \text{m/s} = 50,000 \, \text{Hz} \times \lambda \] Solving for \( \lambda \): \[ \lambda = \frac{1000}{50,000} = 0.02 \, \text{m} = 2 \, \text{cm} \]
Step 4: Conclusion.
Thus, the wavelength of the ultrasound signal in that medium is 2 cm.
Top IIT JAM BT Physics Questions
- Rain is falling vertically with a speed of 40 $m s^{-1}$. Wind starts blowing with a speed of 16 $m s^{-1}$ in the west to east direction. How should a person, who is standing, hold his umbrella to avoid getting wet?
- A massless ideal spring is hanging vertically. A sphere of mass of 500 g, suspended from the spring, stretches the spring from its initial position by 50 cm when it reaches equilibrium. The force constant of the spring is _________ $N m^{-1}$. ($Use g=10 m s^{-2}$)
- Whales can dive undersea to depths of 2 km. The pressure on the whale at this depth (ignoring atmospheric pressure) is _____ $× 10^6 Pa$. (Density of sea water = $1 g cm^{-3}$ and $g =10 m s^{-2}$)
- The heat required to convert 2 kg of water at 20 °C in a calorimeter to steam at 100 °C and at atmospheric pressure (1 atm) is _____ kJ. (Specific heat capacity of water is $4.2 kJ kg^{-1} K^{-1}$ and latent heat of steam is $2256 kJ kg^{-1}$)
- An electron is accelerated from rest through a potential difference of 200 V. The de Broglie wavelength associated with this electron is _____ nm. (Rounded off to 2 decimal places) (Planck’s constant = $6.6 × 10^{-34} J s, 1eV=1.6 × 10^{-19} J$, mass of an electron = $9.1×10^{-31} kg$)
Top IIT JAM BT Speed and velocity Questions
- Rain is falling vertically with a speed of 40 $m s^{-1}$. Wind starts blowing with a speed of 16 $m s^{-1}$ in the west to east direction. How should a person, who is standing, hold his umbrella to avoid getting wet?
- A man throws a ball vertically up in the air with an initial velocity v1 such that it reaches a height of 12 m with a speed of 12 m/s. If he throws the same ball vertically up with an initial velocity v such that it reaches a maximum height of 12 m. Calculate v1/v2 (up to 2 decimal places).
Top IIT JAM BT Questions
- Which one of the following compounds inhibits the polymerization of tubulin to microtubules in animal cells?
- Arrange the following elements in increasing order of their electronegativity according to the Pauling scale
C, Na, Be and Br - Which one of the following is NOT a plant vascular tissue?
- A growing shoot of a germinating seedling encounters an underground obstacle. Which one of the following hormones elicits ‘triple response’ to the underground obstacle?
- Which one of the following pairs of antibodies contains ‘J-chain’ in their multimeric form?