Explain me this in simple manner

It will take approximately 2.14 seconds for the sound wave to travel 1.5 km.

To solve this problem, we first need to find the speed of the sound wave using its frequency and wavelength, and then use that speed to calculate the time taken to cover the given distance.

1. Convert all given values to SI units:

   • Frequency (\(f\)) = 2 kHz = \(2 \times 1000\) Hz = 2000 Hz
   • Wavelength (\(\lambda\)) = 35 cm = \(35 \div 100\) m = 0.35 m
   • Distance (\(d\)) = 1.5 km = \(1.5 \times 1000\) m = 1500 m

   Exam Tip: Always convert all quantities to their standard SI units (metres, seconds, kilograms, Hertz) before performing calculations to avoid errors.

2. Calculate the speed of the sound wave (\(v\)):

   The relationship between speed, frequency, and wavelength is given by the formula:

   \[ v = f \times \lambda \]

   • Substitute the values:
   • \(v = 2000 \text{ Hz} \times 0.35 \text{ m}\)
   • \(v = 700 \text{ m/s}\)

   So, the speed of the sound wave is 700 metres per second.

3. Calculate the time taken (\(t\)) to travel the distance:

   The relationship between speed, distance, and time is:

   \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \quad \text{or} \quad t = \frac{d}{v} \]

   • Substitute the values:
   • \(t = \frac{1500 \text{ m}}{700 \text{ m/s}}\)
   • \(t = \frac{15}{7} \text{ s}\)
   • \(t \approx 2.1428 \text{ s}\)

Therefore, the sound wave will take approximately 2.14 seconds to travel 1.5 km.