Explanation

Explanation

In longitudinal waves, the particles of the medium (air molecules, in this case) vibrate back and forth in the same direction as the wave is moving.

This is how sound propagates through gases like air.

Laplace also corrected Newton's theory by including the effect of adiabatic compression, improving the accuracy of the speed of sound calculation in air.

Explanation

On the spur of the moment Meaning: To do something suddenly, without planning or thinking beforehand.

"I booked a ticket to the concert on the spur of the moment."

Explanation

1. Stone dropped from 400 ft tower — Impact sound heard time:

• What happens: Stone falls, hits water, sound travels back up.

• Key points:

  • Time to fall = $sqrt{frac{2h}{g}} = sqrt{frac{2 times 400}{32}} = 5 text{ seconds}$

  • Time for sound to travel up = $frac{400}{1120} approx 0.36 text{ seconds}$
    

• Total time: Around $5+0.36=5.36$ seconds (approximate).

Explanation

Let the principal = ₹100

Rate = 20% per annum, compounded annually

Now calculate the amount over the years:

After 1 year: 100 × 1.20 = ₹120

After 2 years: 120 × 1.20 = ₹144

After 3 years: 144 × 1.20 = ₹172.80

After 4 years: 172.80 × 1.20 = ₹207.36

So, the amount just exceeds double (₹200) after 4 years.

Explanation

Year 1:

• Start: ₹12,500

• Interest: 20% of ₹12,500 = ₹2,500

• Amount due = ₹12,500 + ₹2,500 = ₹15,000

• After ₹2,000 payment: ₹15,000 - ₹2,000 = ₹13,000

Year 2:

• Start: ₹13,000

• Interest: 20% of ₹13,000 = ₹2,600

• Amount due = ₹13,000 + ₹2,600 = ₹15,600

• After ₹2,000 payment: ₹15,600 - ₹2,000 = ₹13,600

Year 3:

• Start: ₹13,600

• Interest: 20% of ₹13,600 = ₹2,720

• Amount due = ₹13,600 + ₹2,720 = ₹16,320

• After ₹2,000 payment: ₹16,320 - ₹2,000 = ₹14,320

Explanation

The Bayt al-Ḥikmah (House of Wisdom) founded in 830ad in Baghdad.

It was established by Harun Rasheed.

Explanation

Hakim Shaibani was a key lieutenant under Muhammad bin Qasim during the conquest of Sindh in the early 8th century.

 Muhammad bin Qasim sent his trusted commander Abu Hakim Shaibani toward Kanauj 

Additional information 

Muhammad ibn Qasim led the Muslim conquest of Sindh

From Raja Dahir in the battle of Aror.

He was the first Muslim to have successfully captured Hindu territories

And initiated the early Islamic India in 712 AD.

Explanation

Reverberation time is mainly influenced by:

• The volume of the room

• The absorptive properties of surfaces

• The number of sound-absorbing objects or people

While absorption can vary slightly with frequency, the frequency itself is not a primary controlling factor of reverberation time.

Explanation

We use the formula for equal annual installments under compound interest:

Let the installment be Rs. x
Principal (P) = ₹2550
Rate (R) = 4% = 0.04
Time (T) = 2 years
Installments are paid at the end of each year.

Using the formula for compound installment repayment:

$$P = frac{x}{(1 + r)^1} + frac{x}{(1 + r)^2}$$

Substitute values:

$$2550 = frac{x}{1.04} + frac{x}{(1.04)^2}$$$$2550 = frac{x}{1.04} + frac{x}{1.0816}$$

Take LCM or solve directly:

$$2550=x(\frac{1}{1.04}+\frac{1}{1.0816})$$

$$2550 = x left(frac{1}{1.04} + frac{1}{1.0816} right)$$$$2550=x(0.9615+0.9246)=x(1.8861)$$

$$2550 = x (0.9615 + 0.9246) = x (1.8861)$$$$x = frac{2550}{1.8861} ≈ 1352$$