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The wavelength of a wave of the frequency is increased to 784 Hz will be 0.57 metre.
The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The given data in the problem is;
f₁ is the frequency of a sound wave in case 1 = 196 Hz
[tex]\lambda[/tex]₁ is the wavelength for the = 1.76 meters.
f₂ is the frequency of a sound wave in case 2 = 784 Hz
[tex]\lambda_2[/tex] is the wavelength for case 2=?
The speed of the wave for the same medium is same which is given as;
[tex]\rm v = \lambda_1 f_1 \\\\ \rm v = 1.76 \times 196 \\\\ \rm v =344.96\ m/sec[/tex]
For case 2;
[tex]\lambda_2 = \frac{v}{f_2} \\\\ \lambda_2 = \frac{344.96}{784} \\\\ \lambda_2=0.44[/tex]
Hence the wavelength of a wave of the frequency is increased to 784 Hz will be 0.57 metre.
To learn more about the wavelength refer to the link;
brainly.com/question/7143261