Waves

To solve this problem, we need to find the beat frequency perceived by each driver as the two cars approach each other. The relevant concept is the Doppler Effect, which describes the change in frequency due to the relative motion between the source and the observer.

Step 1: Understand the Given Data.

Both cars travel at 7.2 km/h, which needs to be converted into meters per second:

7.2 km/h = (7,200 m/3,600 s) = 2 m/s.

Each horn has a frequency of Hz. The speed of sound in air is m/s.

Step 2: Calculate the apparent frequency heard by each driver.

Since both cars are moving towards each other, the Doppler Effect causes an increase in the frequency heard by each driver. The formula for the observed frequency when both source and observer move towards each other is:

where is the observer's speed, and is the source's speed. In this case, m/s. Thus, the formula becomes:

Calculate :

Hz.

Step 3: Determine the Beat Frequency.

The beat frequency is given by the absolute difference between the observed frequency and the original frequency:

Hz.

Since the beat frequency should be an integer, round it to 8 Hz.

Final Answer:

The beat frequency heard by each driver is 8 Hz, which falls within the given range of 8 to 8 Hz.

The correct answer is 3



Therefore , linear mass density is 3 kg/m.

K₁= = ….(i)
and
K₂= ….(ii)
from (i) and (ii) we can say
3K₁ = K₂ – 2φ

The correct answer is 152 Hz
f₁ = f , f₂ = f + 4
f₃ = f + 2 × 4 , f₄ = f + 3 × 4
f₂₀ = f + 19 × 4
= f + (19 × 4) = 2 × f
f = 76 Hz.
Frequency of last tuning forks = 2f
= 152 Hz

The correct answer is (C) : A-IV, B-III, C-II, D-I
Television signal ⇒ 6 MHz
Radio signal ⇒ 2 MHz
High Quality music ⇒ 20 kHz
Human speech ⇒ 3 kHz

Calculation of Amplitude Modulation Parameters:

Step 1: Formula for Maximum and Minimum Amplitude

The maximum amplitude ( ) and minimum amplitude ( ) are given by:

Where:

• : Carrier amplitude
• : Modulating signal amplitude

Step 2: Substitute the Given Values

Given and :

Step 3: Ratio of Maximum to Minimum Amplitude

The ratio is calculated as:

Conclusion:

The ratio of maximum amplitude to minimum amplitude is .

The velocity of longitudinal wave in the rod will be :

=
The Correct Option is (D)

The correct answer is 32
From given equation,
ω = 160 and k = 0.5
∴ Speed of wave,

The correct answer is 400

The fringe width ( ) in a double-slit experiment is given by: where: - is the wavelength of the light, - is the distance between the slits and the screen, - is the separation between the slits.
Step 1: Relation between fringe widths. Since and are constant, the fringe width is directly proportional to :
Step 2: Calculate the new fringe width. Let the initial fringe width ( ) correspond to and the new fringe width ( ) correspond to . Then: Substituting , , and :
Final Answer: The fringe width for is:

The fundamental frequency ( ) of a vibrating string is given by: where: \item is the frequency, \item is the wave velocity, \item is the length of the string.
Step 1: Relation between frequencies and lengths. For the initial string length ( ) and frequency ( ): For the new string length ( ) and frequency ( ): Taking the ratio of the two frequencies: Substitute and : Simplify: Rearrange to solve for :
Step 2: Substitute the initial length. Given :
Final Answer: The new string length is:

The power radiated by a linear antenna is proportional to the square of the current and the square of the antenna's length. Additionally, the radiated power depends inversely on the square of the wavelength of the electromagnetic wave. Thus, the proportionality relation is:
Final Answer: The power radiated from a linear antenna is proportional to:

Step 1: Formula for Frequency

The frequency of a vibrating string is given by:

where:

• : Length of the string
• : Tension in the string
• : Linear mass density of the string.

Step 2: Substitute Tension in Terms of Young’s Modulus

The tension can be expressed in terms of Young’s modulus ( ) as:

where:

• : Young’s modulus
• : Cross-sectional area of the string
• : Extension of the string
• : Original length of the string.

Substitute into the frequency formula:

Step 3: Substitute the Given Values

Substitute the numerical values:

• .

Substitute into the formula:

Step 4: Simplify the Expression

Simplify the terms inside the square root:

Simplify further:

Final Answer:

The frequency of the vibrating string is .

The threshold wavelength ( ) for a metal surface is related to its work function ( ) by the equation:

where:

• is Planck's constant,
• is the speed of light,
• is the work function of the metal.

Given:

Step 1: Calculate Threshold Wavelengths for Both Metals

For Metal A:

For Metal B:

Step 2: Determine the Difference Between Threshold Wavelengths

Therefore, the difference between the threshold wavelengths for metal surfaces A and B is 138 nm, which corresponds to option (4).

Optical communication is performed in the frequency range of 1 THz to 1000 THz (from Microwave to UV). Therefore, the wavelength of EM waves used for optical communication is shorter than that of microwaves used in Radar. Hence, Assertion A is incorrect. On the other hand, Reason R is true because infrared waves have higher frequency and energy compared to microwaves. Thus, Assertion A is false but Reason R is true. Therefore, the correct answer is .

Understanding the Problem

We are given the condition for the first minimum in single-slit diffraction and need to find the slit width ( ).

Solution

1. Condition for First Minimum:

The condition for the first minimum in single-slit diffraction is:

where:

• is the slit width
• is the angle of the minimum
• is the wavelength of light

2. Substitute Values:

Given and , we have: