To hear a distinct echo in air, the reflecting surface must be at a minimum distance of about:

The correct answer is B, 600 m. The speed of a wave is the product of its frequency and its wavelength, so the speed here is 50 hertz multiplied by 4 metres, that is 200 metres per second. Distance is speed multiplied by time, so in 3 seconds the wave covers 200 multiplied by 3, which is 600 metres. Always find the speed first and only then apply the time.

Option A, 100 m, would follow from dividing rather than multiplying somewhere in the working. Option C, 200 m, is the distance covered in one second and is the answer to a different question; it is the speed, not the answer asked for. Option D, 300 m, corresponds to no correct step at all and is included because it resembles the rounded speed of sound in air, which is irrelevant here since the speed is given indirectly by the data.

The correct answer is C, Pitch. Pitch is the characteristic of a sound by which the brain judges it as shrill or flat, and it is decided by the frequency of the wave. A higher frequency is heard as a higher pitch, which is why a woman's voice or a whistle sounds shriller than a drum or a man's voice. The physical quantity is frequency; the sensation produced in the brain is pitch.

Option A, wavelength, is the distance between two successive compressions and is a measurement of the wave in space, not a sensation. Option B, wave velocity, depends on the medium and its temperature and is the same for a shrill and a flat sound in the same air. Option D, oscillation, simply means one complete to and fro vibration; counting oscillations per second gives frequency, but the word itself names no property that the brain interprets.

The correct answer is D, 2 s. Convert the units first: 1 kilohertz is 1000 hertz and 50 centimetres is 0.5 metre. The speed is frequency multiplied by wavelength, that is 1000 multiplied by 0.5, which gives 500 metres per second. Time equals distance divided by speed, so 1000 metres divided by 500 metres per second gives 2 seconds.

Option A, 5 s, would follow from using a speed of 200 metres per second. Option B, 4 s, corresponds to a speed of 250 metres per second, which arises if the wavelength is halved by mistake. Option C, 3 s, is close to the time sound actually takes to cover a kilometre in ordinary air, about 340 metres per second, and is the trap for candidates who use the remembered speed of sound instead of the speed calculated from the data given.

The correct answer is B, the amplitude of the sound waves. Amplitude is the maximum displacement of a particle of the medium from its rest position, and the energy carried by a wave increases with the square of the amplitude. A larger amplitude therefore delivers more energy to the ear and is heard as a louder sound. Loudness is measured in decibel.

Option A, the velocity of the wave, is fixed by the medium and its temperature; a loud and a soft sound in the same room travel at exactly the same speed. Option C, frequency, decides pitch, that is whether the sound is shrill or flat, and not how loud it is; turning up the volume of a ringtone does not change its frequency. Option D combines two quantities that both govern properties other than loudness, so it is wrong for the same reasons.

The correct answer is B, light travels much faster than sound. The flash and the clap are produced at the same instant by the same discharge. Light covers about three lakh kilometres in one second, so it reaches the observer almost immediately, while sound in air covers only about 340 metres in a second and takes roughly three seconds for each kilometre. The gap between seeing and hearing is therefore a direct measure of distance.

Option A reverses the true order and would make thunder arrive first, which never happens. Option C is wrong because equal speeds would make the flash and the clap arrive together, with no gap at all. Option D confuses brightness with speed; the flash is indeed very bright, but intensity has nothing to do with why it arrives earlier, and even a faint flash would still be seen before the sound was heard.