Final answer:
The correct options are (b) r and s. The sound wave is not produced inside the string but rather in the surrounding air. Sound waves in the string are longitudinal, not transverse. The wavelength of the sound wave in the surrounding air is equal to the wavelength of the transverse wave on the string. The loudness of sound is proportional to the square of the amplitude of the vibrating string.
Step-by-step explanation:
The correct options out of the given statements are (b) r and s.
Statement (p) is incorrect because the sound wave is not produced inside the string but rather in the surrounding air. The vibrating metallic string transfers energy to the air, creating compressions and rarefactions that move out as longitudinal pressure waves.
Statement (q) is also incorrect because sound waves in the string are longitudinal, not transverse. Transverse waves on the string are responsible for creating the vibrations but the resulting sound wave is longitudinal.
Statement (r) is correct. The wavelength of the sound wave in the surrounding air is equal to the wavelength of the transverse wave on the string. This is because the frequency of the sound wave is determined by the vibrating string, and the wavelength is inversely proportional to the frequency.
Statement (s) is correct. The loudness of sound is indeed proportional to the square of the amplitude of the vibrating string. A higher amplitude of vibration leads to a larger displacement of air molecules, resulting in a louder sound.