Sound Wave

Step 1: Concept
The Doppler Effect describes the change in frequency due to relative motion.
Step 2: Analysis
Apparent frequency . Since the denominator is smaller than , .
Step 3: Conclusion
The frequency heard by the observer is higher than the source frequency.
Final Answer: (A)

Step 1: Concept
Velocity of sound (where is in Kelvin).
Step 2: Analysis
. .
Step 3: Conclusion
The velocity is approximately 348 m/s.
Final Answer: (B)

Step 1: Moles at Equilibrium
used = 60% of 5 = 3 moles. Reaction: . Remaining . used = . Remaining . formed = 3.
Step 2: Total Moles
Total moles at equilibrium = .
Step 3: Partial Pressure
. atm.
Final Answer: (d)

Step 1: Impurity Problem
In the contact process for manufacturing sulphuric acid, arsenic impurities can poison the catalyst.
Step 2: Mechanism
Arsenic impurity typically exists as a negative sol ( ).
Step 3: Purification
is a positive sol. It is used to neutralize and remove the negatively charged arsenic sol from the gas stream.
Final Answer: (a)

Step 1: Concept
Beats , where frequency .
Step 2: Equation
.
Step 3: Solving
.
Final Answer: (A)

Step 1: Understanding the harmonics in open and closed pipes.
- For an open pipe, the fundamental frequency is given by: where is the velocity of sound and is the length of the pipe. The harmonics for an open pipe are integer multiples of the fundamental frequency.
- For a closed pipe, the fundamental frequency is lower, and its harmonics are only odd multiples of the fundamental frequency. For the third harmonic of the closed pipe to be higher than the fundamental frequency of the open pipe by 100 Hz, we can set up an equation based on the difference in frequencies.

Step 2: Solving for the fundamental frequency of the open pipe.
- Let the fundamental frequency of the open pipe be . The frequency difference for the third harmonic of the closed pipe is 100 Hz. So, the difference in frequencies is: This gives , and by calculating the frequencies, we can deduce that the fundamental frequency of the open pipe is .

Step 3: Conclusion.
The fundamental frequency of the open pipe is 200 Hz. Hence, the correct answer is (1).

Step 1: Understanding the Concept:
Average velocity = .
Step 2: Detailed Explanation:
Let each time interval be . Displacement in first interval = , in second = .
Total displacement = . Total time = .
Average velocity = .
Step 3: Final Answer:
Thus, average velocity = .

Concept: Doppler effect for moving observer:

Step 1: Observer moving towards source.
Use plus sign.

Step 2: Final expression.

Concept:

Step 1: Change in frequency.
If length increases by , frequency decreases by :

Step 2: Beat frequency.


Step 3: Case analysis.
Since initially in unison, fork frequency = Now: But this gives lower frequency case. Actual fork frequency is slightly higher:

Concept:

Step 1:Apply changes:
•
•
•

Step 2:Substitute:

Step 3:Simplify: Since ,